What is the difference between 'stochastic' and 'probabilistic'?

I think most people use them as synonyms. In general usage, it can be appropriate. However, a probabilistic approach describes the occurrence of deterministic states with given probabilities, while stochastic processes are built up by sequential steps occurring with given probabilities.

Think of the difference between throwing a die once which determines the state you will arrive at and throwing a die multiple times where the resulting states are (can be) dependent on the previous states.