Kinetic Fokker-Planck Equation vs Kramers Equation Is there any difference between the Kinetic Fokker-Planck Equation and Kramers Equation ? I have seen them both used as a name for the Kolmogorov forward equation describing the time evolution for the distribution of the velocity and position of a particle (e.g living in some solvent).
Does the different choice in name have any meaning?

Well, there are several stochastic process with several different names. Maybe, as you said, the Kinetic Fokker-Planck Equation is just the Kramers equation, which is basically a Brownian particle in the phase space, i.e, in the space of position $X$ and momentum $P$. In this equation, the kinetic term is taken into account, which is the first term in the following PDE:
\begin{align}
\frac{\partial \rho}{\partial t} = -\frac{P}{M}\left[\frac{\partial  \rho}{\partial X}\right]+ \gamma\left[\frac{\partial  \left(P\rho\right)}{\partial P}\right]  +D\left[\frac{\partial^2  \rho}{\partial P^2}\right].
\end{align}
For example, take a look in the following reference eq. 1.1) https://arxiv.org/pdf/1905.05994.pdf
