The book from Sutton and Barto, Reinforcement Learning: An Introduction, define a model in Reinforcement Learning as
something that mimics the behavior of the environment, or more generally, that allows inferences to be made about how the environment will behave.
In this answer, the answerer makes a distinction:
There are broadly two types of model:
A distribution model which provides probabilities of all events. The most general function for this might be $p(r,s'|s,a)$ which is the probability of receiving reward $r$ and transitioning to state $s'$ given starting in state $s$ and taking action $a$.
A sampling model which generates reward $r$ and next state $s'$ when given a current state $s$ and action $a$. The samples might be from a simulation, or just taken from history of what the learning algorithm has experienced so far.
The main difference is that in sampling models I only have a black box, which, given a certain input $(s,a)$, generates an output, but I don't know anything about the probability distributions of the MDP. However, having a sampling model, I can reconstruct (approximately) the probability distributions by running thousands of experiments (e.g. Monte Carlo Tree Search).
On the other hand, if I have a distribution model, I can always sample from it.
I was wondering if
what I wrote is correct;
this distinction has been remarked in literature and where I can find a more in-depth discussion on the topic;
someone has ever separated model-based algorithms which use a distribution model and model-based algorithms which use only a sampling model.