In ; Stochastic's, SDE, PDE, I have heard the terminology $\textit{"Diffusion Model" or "Diffusion Equation"}$.
The heat equation is sometimes also called the Diffusion Equation ( since it represents the diffusion of heat over some domain, or since its built from Brownian Motion which describes the random trajectories of a brownian particle ). I assume this is just lazy and the heat equation is just a 'very particular diffusion equation'.
Can anyone explain what someone is referring to when they talk about $\textit{'a Diffusion Equation, or the Diffusion Part of the Equation'}$. If anyone can explain this from a mathematical or physical perspective that would be amazing.
Note see Relationship between the diffusion equation and the heat equation for a closely related discussion.