For example, why is the semileptonic $B$ decay $B \to X\ell\nu$ inclusive?
I can't find any definition of these frequently used terms, strange.
[Physics] What’s the difference between inclusive and exclusive decays
particle-physicsterminology
Related Solutions
A perturbation is a small change (usually deterministic and known), while a fluctuation is a (not necessarily small) random perturbation with mean zero (and therefore either unknown or unrepeatable).
Usually one talks about a perturbation in the context of perturbation theory. Perturbation theory is used to study a system that is slightly different from a nice system where you can do calculations easily; the difference from the nice system is the perturbation.
On the other hand, one talks about fluctuations when deriving results for the mean of certain quantities; the fluctuations are the deviations from the mean. Another common word for fluctuations is noise (used in the singular only). In realizations of stochastic processes, fluctuations are visible as contributions of large but irregular frequency, whereas a perturbation would be in this context a small change of a parameter of the system or the forcing term.
Joule heating is typically associated with increases in random kinetic energy (i.e., heat) due to $\mathbf{j} \cdot \mathbf{E}$. Ohmic dissipation and resistive heating are similar in a sense to Joule heating, as all three result from fluctuating electric fields acting as an effective drag force on an otherwise free flowing charged particle.
Ion drag is likely associated with fluid terms like viscosity or Coulomb collisions, which can act to inhibit the bulk flow of charged particles.
Generally in a plasma, one refers to anomalous resistivity or anomalous viscosity. The use of the word anomalous comes from the fact that the interactions are not rigorously fluid-like (i.e., not from collisions). They are typically the result from a wave or fluctuating fields radiated by an instability that then act to remove the free energy that created them. Note that I am not referring to the "fudge factor" that MHD simulations will often use to account for or introduce some form of dissipation.
These terms are used in MHD, though in a plasma we have found through observation and particle-in-cell (PIC) simulations that resistive/drag terms arise from purely kinetic effects. Meaning, to have these effects in MHD is to artificially insert them (i.e., throw in some adaptive anomalous resistivity or allow numerical resistivity).
I will edit this answer later with a more thorough response, but my newborn just woke up and needs attention.
Edit/Additions
The $\mathbf{j} \cdot \mathbf{E}$ comes from Poynting's theorem where: $$ \partial_{t} W_{EM} + \nabla \cdot \mathbf{S} = - \mathbf{j} \cdot \mathbf{E} $$ where $W_{EM}$ is the electromagnetic energy density (= $\varepsilon_{o} E^{2}/2$ + $B^{2}/(2 \ \mu_{o})$) and $\mathbf{S}$ is the Poynting flux (= $\mathbf{E} \times \mathbf{B}/\mu_{o}$). Another way to say this is the time rate of change of the energy density of the electromagnetic fields plus the rate of electromagnetic energy flux flowing out of a surface equals the energy lost due to momentum transfer between particles and fields.
When you can approximate $\mathbf{E}$ as $\overleftrightarrow{\eta} \cdot \mathbf{j}$, where $\overleftrightarrow{\eta}$ is a resistivity tensor, then we have: $$ \mathbf{j} \cdot \mathbf{E} \rightarrow \mathbf{j} \cdot \overleftrightarrow{\eta} \cdot \mathbf{j} $$ which is often approximated to be ~$\eta \ j^{2}$, where we have reduced the tensor to a scalar. In this form, one would call this Ohmic heating or resistive heating. I think of it this way because the conversion of $\mathbf{E}$ to a function of $\mathbf{j}$ is referred to as Ohm's law.
Drag Force
Drag forces are often written in a form similar to:
$$
\mathbf{F} = - b \ \mathbf{v}
$$
where $b$ is a constant and $\mathbf{v}$ is the velocity of the object experiencing the drag. In a collisional medium, $b$ $\rightarrow$ $m \ \nu$, where $m$ is the mass of the object and $\nu$ is a characteristic frequency which is a collision rate in this case.
The advantage of this form, $\mathbf{F}$ = -$m \ \nu \ \mathbf{v}$, is that $\nu$ can be applied to binary collisions, Coulomb collisions, or wave-particle collisions (what I referred to as anomalous collisions before).
Relation to Resistivity
The collision frequency can be related to resistivity by:
$$
\eta = \frac{ m \ \nu }{ n_{e} \ e^{2} }
$$
where $n_{e}$ is the electron number density and $e$ is the fundamental charge. In the ionosphere, the dominant resistive terms arise from electron-neutral and electron-ion collisions. In the solar wind, however, the Coulomb collision rates are roughly one per day near Earth (assuming $90^{\circ}$ deflections, i.e., not including small angle deflections). So in the presence of a waves/instabilities, the dominant terms arise from wave-particle collisions where the wave fields act as scattering centers.
The proper form for the wave-particle collision rate depends upon the dispersion relation for the wave. In the quasi-linear approximation for ion-acoustic waves, for instance, the anomalous collision frequency is given by: $$ \nu = \omega_{pe} \frac{ \varepsilon_{o} \ \delta E^{2} }{ 2 \ n_{e} \ k_{B} \ T_{e} } $$ where $\omega_{pe}$ is the electron plasma frequency, $\delta E$ is the wave electric field, $k_{B}$ is the Boltzmann constant, and $T_{e}$ is the electron temperature.
Summary
I think the best thing to do is explicitly state the term(s) that you are referring to in your work. Meaning, write out $\mathbf{j} \cdot \mathbf{E}$ as the definition of Joule heating, for instance. If you explicitly show the term to which you refer, you will not have an issue. The confusion largely arises from implied relationships between the jargon and the actual mathematical expressions that are used incorrectly or carelessly.
I also agree with Vytenis, in that the frame of reference for which you define these terms is critical because both $\mathbf{j}$ and $\mathbf{E}$ depend upon the frame of reference. However, if you clearly define each of the terms to which you refer, this should not be an issue either.
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Best Answer
An experimental take
Exclusive implies that you have measured the energy and momenta of all the products (well, with an exception I'll discuss below). Inclusive means that you may have left some of the products unmeasured.
This applies to scattering processes as well as decays.
Some things to note:
In the process you are asking about the neutrino is necessarily unobserved rendering the measurement inclusive, further an $X$ in the final state is often used to indicate unmeasured and unspecified stuff (i.e. it means the measurement is inclusive by design). Here unspecified includes case in high acceptance instruments where you consider all events with the specified products: those for which we know $X$ is empty, those for which $X$ is non-empty and well characterized, and those for which $X$ is ill-characterized.
Theoretical view
I'm less sure of how theorist use these terms, but I believe there is a parallel. Something like: exclusive means one and only one process, while inclusive means all processes that include the specified products.
Convergence of theory and experiment
Of course, we haven't really learned anything until we get theory and experiment together, which is sometimes traumatic for both communities. Still exclusive measurements and calculations are clearly talking about the same thing, and inclusivity can be made to agree with some care in building the experiment and assembling the theoretical results.
Experimenters cheating on exclusivity
Sometimes in nuclear physics we talk about scattering measurements as exclusive when there is an unmeasured, heavy, recoiling nucleus involved. The assumption being that that it carries a small fraction of the total energy and momentum involved and can be neglected, though there is some risk from this if the nucleus is left in a highly excited state.
In particular my dissertation project was on $A(e,e'p)$ reaction (elastic scattering of protons out of a stationary nuclear target where the beam was characterized and both the proton and outgoing electron were observed), and we assumed that the remnant nucleus was left largely undisturbed and recoiling with a momentum opposite the Fermi motion of the target proton.