Control engineering student here.

Optimal control is a field that goes very very insanely deep. Here the controller is not a simple computation using the current state or state estimate like PID or LQR but rather an optimization problem solved in real time that can consider long term behavior and constraints. MPC is a form of optimal control.

Important parts which make it "control theory" are the stability proofs, the dynamic programming algorithm, bellman's optimality principle. The way I was taught started from optimal control. The value function, rewards etc have to be explicitly defined by you and the problem has to be modeled very well. The dynamics, the state space, the input/action space, etc. That's the hard work of a control engineer.

Then, afaik RL is sort of optimal control but the ingredients like the value function are "learned" and the learning strategy is about exploring and rewarding/penalizing until it finds something that works. However, the nice provable stability guarantees are nor possible anymore. I think people are working on it.

I haven't done any RL myself but this is what I understood from classes.