As a supplement to nbro's nice answer, I think a major difference between RL and optimal control lies in the motivation behind the problem you're solving. As has been pointed out by comments and answers here (as well as the OP), the line between RL and optimal control can be quite blurry.
Consider the LQG algorithm (linear quadratic gaussian) which is generally considered to be an optimal control method. Here a controller is computed given a stochastic model of the environment and a cost function.
Now consider AlphaZero, which is obviously thought of as an RL algorithm. AlphaZero learns a value function (and thus a policy/controller) in a perfect information setting with a known deterministic model.
So it's not the stochasticity that separates RL from optimal control as some people believe. It's also not the presence of a known model. I argue that the difference between RL and optimal control comes from the generality of the algorithms.
For instance, generally when applying LQG and other optimal control algorithms, you have a specific environment in mind and the big challenge is modeling the environment and the reward function to achieve the desired behavior. In RL on the other hand, the environment is generally thought of as a sort of black box. While in the case of AlphaZero the model of the environment is known, the reward function itself was not designed specifically for the game of chess (for instance, it's +1 for win and -1 for loss regardless of chess, go, etc). Furthermore the neat thing with AlphaZero is that we can use it to train agents in virtually any perfect information game without changing the algorithm at all. Another difference with RL here is that the agent iteratively improves itself, while optimal control algorithms learn controllers offline and then stay fixed.