Before I get roasted in the comments, let me say I recently got a BS in electrical engineering, so I’m not a newbie in these concepts. I’ve studied electric potential energy, electric potential, voltage (a.k.a. electric potential difference, electric tension, electric pressure), time-varying/non-conservative electromagnetic fields, Maxwell’s equations, etc. I’ve read textbooks on university physics, on electromagnetic theory, on circuit analysis/theory. (But I haven’t studied quantum mechanics or relativity.)
Before explaining why I think voltage and electric potential actually describe the same physical phenomena/process, first I’ll briefly recall certain facts about the two, so that you can see I have some standard understanding on these concepts.
Electric potential
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Electric potential is the electric potential energy, per unit charge, at a point in space. Recall that electric potential energy is a type of potential energy (i.e. energy that a particle has by virtue of its position in space or in a field, it is energy that could be used to do work), associated with the position of a charged particle.
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Electric potential is defined at a point in space, provided we’ve previously defined the zero electric potential point (usually Earth ground or a point infinitely far from the region of space under study). Since the potential is defined at any point in space (at least for conservative electric fields), and since it is a scalar value at each point, then we say the electric potential is a scalar field. It makes perfect sense. I can say “the electric potential at point $P_0$ is $\phi_0$”.
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We sometimes use the electric potential (a scalar field) to calculate a static electric field (a vector field) as the negative of the gradient of the electric potential, because the former is easier to calculate than the latter.
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Electric potential is the quantity in which Laplace's equation and Poisson's equation are described.
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We can plot the electric potential as a 2D or 3D scalar field.
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We can write Maxwell’s equations in terms of the electric potential and the magnetic vector potential.
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Physicists use the term electric potential more often than voltage.
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Etc.
Voltage or electric potential difference
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Voltage is defined as the work to be done (or energy to be transferred), per unit charge, to move a charged particle with unit charge, from one point in space to another point in space, along some path or trajectory. So voltage is a quantity between two points, while electric potential is a quantity at a single point.
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In the presence of conservative electric fields only, voltage can also be calculated as the difference of the electric potential at the two points, thus the name electric potential difference.
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Voltage is usually thought of as a scalar, without being a (scalar) field like electric potential. It makes perfect sense. I can say “the voltage between point (or node in the context of circuits) $a$ and point $b$ is $V_{ab}$”. But it wouldn’t make sense to say “the voltage at point $c$ is $V_c$”, because we’re not specifying with respect to which other point we’re measuring it, unless it is implicitly obvious.
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Voltage (and current), not electric potential, is the quantity in which Ohm’s law, the voltage-current relationship for inductors, capacitors, and diodes, are written.
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Voltage, not electric potential, is the quantity in which Kirchhoff’s voltage law is described.
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In the presence of conservative electromagnetic fields only (zero currents [electrostatics] or constant currents [magnetostatics]), the work to be done between two points is independent of any of the possible paths connecting the two points, and so the work to be done in moving a charge around a closed loop is zero, and since voltage is work per charge, then voltage is also independent of path in such case. But in the presence of non-conservative electromagnetic fields (time-varying currents [electrodynamics], for example AC circuits, with non-negligible leakage electromagnetic fields outside circuit elements/devices such as inductors), the work to be done in moving a charge from one point to another does depend on the path, and so the work to be done in moving a charge around a closed loop is in general not zero, and so voltage also depends on the path.
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Electrical/electronics engineers use the term voltage more often than electric potential.
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Etc.
Why I think voltage and electric potential are the same
Okay, now to my question. I recently had an online discussion with someone, where I said voltage and electric potential were not the same, while the person said they were. I explained them in a similar manner I just did above. But after talking and me thinking, I think those two quantities are really describing the same thing. Below I’ll try to convince you, or at least explain you why to me those quantities seem the same.
Suppose I choose one point in space, which I’ll call the reference point, with respect to which I measure the voltage at all other points in space. Isn’t that, then, the same as electric potential? For example, I could choose the reference point to be the Earth ground or a point infinitely far from us, thus the voltage would seem to have the same meaning as electric potential.
And since I’ve chosen one reference point for voltage measuring, then at each point in space the voltage has a certain scalar value. Thus voltage is now a scalar field, like electric potential. So, we can also compute a conservative electric field from this voltage “field”, and we can write Maxwell’s equations in terms of this voltage “field” (and the magnetic vector potential), just like we could with the electric potential.
And this idea of choosing a reference point for voltage measuring is not uncommon. It is widely used in a method of circuit analysis known as nodal analysis; all or most circuit simulators use that method; it is also used in power systems analysis to obtain the admittance matrix that mathematically describes the electrical behavior of a power system; even using oscilloscopes in real-life electronic circuits is the same, because we attach the negative probe to one node (usually called ground in electronics) of the circuit and then only move the positive prove for measuring the voltage.
So, as you can see, the electric potential at a point is the voltage measured at that point with respect to the zero-potential reference point, so potential is the same as voltage. Or equivalently, the voltage measured between any two points $a$ and $b$ is the electric potential at point $a$ by choosing the zero-potential reference point to be point $b$ (in other words, to obtain voltage from potential, the zero-potential point is not fixed for measuring all potentials), so voltage is the same as potential.
Please note I’m suggesting that voltage (electric tension, electric pressure, electric potential difference) and electric potential are the same thing, not that any of them is the same as electric potential energy. I know the former two are not the same as the latter.
I searched if this question had been already asked, but didn’t find any. I found the following which ask different questions:
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Difference between voltage, electrical potential and potential difference
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Is voltage electric potential or electric potential difference?
Edit after accepted answer: further clarification on why I say voltage and potential are the same
So far some people have answered/commented that the difference between electric potential and voltage is that the latter is a difference in potentials (which is true), in other words, that voltage is between two points (which is true) while potential is only at one point (which is not exactly true). Let me explain. You may say potential is a quantity only a point, right? Well, if you please look at equations (2.21) (for electric potential) and (2.22) (for electric potential difference, a.k.a. voltage) of David Griffiths' Introduction to Electrodynamics (3rd edition), both on page 78, you will see Griffiths defines electric potential and electric potential difference (a.k.a. voltage) as follows. (In the same manner as Roger's answer, and unlike Griffith, I'll denote voltage as $V$ and electric potential as $\phi$.)
$\phi = – \displaystyle\int_{\mathcal O}^{\mathbf r} {\mathbf E} \cdot {\mathrm d} {\mathbf l} \tag {2.21}$
$V_{ab} = \phi(\mathbf a) – \phi(\mathbf b) = \displaystyle\int_{\mathbf a}^{\mathbf b} {\mathbf E} \cdot {\mathrm d} {\mathbf l} \tag {2.22}$
Now look at the rightmost-hand side of both equations. They both are the line integral of the electric field vector from one point to another point along some path or trajectory. Aha! So electric potential is in general a quantity between two points, just like voltage!
Yes, I know that for electric potential (eq. 2.21), we usually choose the zero-potential reference point $\mathcal O$ to be at infinity, so that the potential then is a quantity at a point. But we can also choose the reference point $\mathbf b$ in the voltage (eq. 2.22) to be also at infinity (if you disagree, please explain), so that voltage is now also a quantity at a point. And as I said earlier, it is actually very common in electrical engineering to talk about the voltage at a point in electric circuits, because we choose one node as the reference node (a.k.a. ground), with respect to which we measure all voltages at the other non-reference nodes.
After discussing with Roger in the comments of his answer, it looks like indeed voltage and electric potential are the same thing, but simply different names for the same thing depending on context (engineering or physics, respectively), with the only tiny difference being that all potentials are measured with respect to a fixed reference point, while voltage can be measured with respect to an arbitrary point (although in nodal analysis we also fix such reference point to be a node, similar to potential).
Edit 2: Why my question is not this question
I've got two suggestions saying that my question is the same as the linked question in the subtitle, so I'll explain why it's not the same question. I'll refer to user11266's answer.
The first and third paragraph of user11266's answer only talk about the reason for confusion in the two terms, and what should be done instead, so those paragraphs are irrelevant to my question.
The second paragraph of user11266's answer talks about potential and potential difference (a.k.a. voltage). He/she says "Each point in space has assigned to it a value for electric potential", which is true because from Griffiths' equation (2.21) it is clear that, for a fixed reference point $\mathcal O$, the potential depends on $\mathbf r$. But guess what? You can also fix $\mathbf b$ in Griffiths' equation (2.22) (potential difference a.k.a. voltage), and now you have the exact same thing as potential: a scalar value at each point in space. And in case you say "no-one fixes a point for measuring voltage", then let me tell you that's actually extremely common: 1) we use it for nodal analysis, the most used method for solving circuits; 2) all circuit simulators use it; and 3) oscilloscopes read voltages by fixing the reference point.
And yes, I know that in the potential equation (2.21) the reference point $\mathcal O$ is usually at infinity, while in my example of circuits the reference point $\mathbf b$ for the voltage equation (2.22) is not at infinity but instead a node of the circuit. But as far as I know, there's nothing prohibiting us from choosing $\mathbf b$ to be also at infinity, in which case equations (2.21) and (2.22) become the same, and thus voltage and potential are the same thing.
And in case you say "potential is more general than voltage because voltage only applies to circuits, so your circuit example is not valid", my reply would be that simply ignore my examples, and instead focus on equation (2.22) from Griffiths and set $\mathbf b = \mathcal O$ and $\mathbf a = \mathbf r$, then swap the integral bounds/limits by adding a negative sign in front of the integral, and now you get $V_{ab} = \phi$. Et voilà, voltage is the same as potential, or potential is the same as voltage, so they're the same thing. Thus my statements in the previous paragraph hold.
Best Answer
In physics voltage is usually defined as potential difference between two points of a circuit: $$V_{ab}=\phi_a-\phi_b.$$ In other words:
One typically has the same reference point for all the potentials, but voltages can be defined between any two points.
Finally, potential is an extremely general concept, used to describe electric and electromagnetic phenomena well beyond circuit theory, whereas voltage is a term mainly limited to specific applications.
Update
The question has been further discussed in the comments, and it was agreed that much of my answer indeed reiterates the information already given in the OP. I therefore state below the main point, as it came out of the discussion: