I think this picture answers the question:
![CuZn battery](https://i.stack.imgur.com/yC7Op.gif)
The battery's terminals are not charged. It's just a chemical reaction that starts the charge.
There's a $\text{Zn}$ and a $\text{CuSO}_4$. When they meet each other via a cable, the $\text{Zn}$ gives 2 electrons to $\text{CuSO}_4$ and becomes $\text{Zn}^{2+}$.
$\text{Cu}^{2+}$ of $\text{CuSO}_4$ becomes $\text{Cu}$ and becomes electrostatically neutral, and separates from $\text{SO}_4^{2-}$.
Then we have $\text{SO}_4$ with -2 charge and $\text{Zn}$ with +2 charge. So, $\text{SO}_4^{2-}$ moves to $\text{Zn}^{2+}$ to get bound to each other.
In the end, we have $\text{ZnSO}_4$ and $\text{Cu}$.
With two different batteries, it's not possible. The $\text{SO}_4^{2-}$ has nowhere to go and make new connections. Thus the chemical and electrical process doesn't start.
Electric current is not a flow of energy; it's a flow of charge. Charge and energy are two very different things.
An electric current is a flowing motion of charged particles, and the *particles do not carry energy*
along with them as they move. A current is defined as a flow of charge by I=Q/T; amperes are coulombs of charge flowing per unit time. The term "Electric Current" means the same thing as "charge flow." Electric current is a very slow flow of charges, while energy flows fast. Also, during AC alternating current the charges move slightly back and forth while the energy moves rapidly forward.
Electric energy is quite different than charge. The energy traveling across an electric current is made up of waves in electromagnetic fields and it moves VERY rapidly. Electric energy moves at a completely different speed than electric current, and obviously they are two different things flowing in wires at the same time. Unless we realize that two different things are flowing, we won't understand how circuits work. Indeed, if we believe in a single flowing "electricity," we will have little grasp of basic electrical science.
In an electric circuit, the path of the electric charges is circular, while the path of the energy is not. A battery can send electric energy to a light bulb, and the bulb changes electrical energy into light. The energy does not flow back to the battery again. At the same time, the electric current is different; it is a very slow circular flow, and the electric charges flow through the light bulb filament and all of them flow back out again. They return to the battery.
Electric energy can even flow in a direction opposite to that of the electric current. In a single wire, electric energy can move continuously forward while the direction of the electric current is slowly backwards. In AC circuits the energy flows continuously forward while the charges are alternating back and forth at high frequency. The charges wiggle, while the energy flows forward; electric current is not energy flow.
for more information visit this website
http://amasci.com/miscon/eleca.html#current
William J. Beaty Electricity Misconceptions
Best Answer
Electric current is the rate of flow of electric charges across any cross-sectional area of a conductor. The direction of electric current is taken as the direction of flow of positive ions or opposite to the direction of flow of free electrons. Your assumption is not necessary here... Electrons always flow from negative terminal to positive terminal.
$$i=\frac{dq}{dt}$$
When current flows through an electrolytic solution or during the process of electrolysis, The plate towards which positive ions (cations) flow is called the cathode and the plate towards which negative ions (anions) flow is called the anode.
Wikipedia says clearly,
So, the convention is totally based on our definition of the direction of current flow that it always flows opposite to the direction of electrons (i.e) electrons can be called as cations or anions depending on the usage. And based on this, we dump our thought that cathode should always be negative, etc...