There are many sub-domains of reinforcement learning, two of which are apprenticeship and imitation learning - but that appears just to be two different names for the same thing?
In general, yes, they are the same thing, which means to learn from demonstration (LfD). But, usually, apprenticeship learning is mentioned in the context of "Apprenticeship learning via inverse reinforcement learning" (IRL). Both methods learn from demonstration, but they learn different things:
- Imitation learning (a.k.a. behavioral cloning) will try to copy the teacher. This can be achieved by supervised learning alone. The AI will try to copy even irrelevant actions such as blinking or scratching, for instance, or even mistakes. You could use RL here too, but only if you have a reward function.
- Apprenticeship learning via inverse reinforcement learning will try to infer the goal of the teacher. In other words, it will learn a reward function from observation, which can then be used in reinforcement learning. If it discovers that the goal is to hit a nail with a hammer, it will ignore blinks and scratches from the teacher, as they are irrelevant to the goal.