I've seen numerous mathematical explanations of reward, value functions $V(s)$, and return functions. The reward provides an immediate return for being in a specific state. The better the reward, the better the state.
As I understand it, it can be better to be in a low-reward state sometimes because we can accumulate more long term, which is where the expected return function comes in. An expected return, return or cumulative reward function effectively adds up the rewards from the current state to the goal state. This implies it's model-based. However, it seems a value function does exactly the same.
Is a value function a return function? Or are they different?