Deterministic environment is one where your agent’s actions uniquely determine the outcome. So, for example, in chess, there’s really no randomness when you move a piece. The effect of moving a piece is completely predetermined, and no matter where I’m going to move the same piece, the outcome is the same. That we call deterministic.
Games with dice, for example, like backgammon, are stochastic. While you can still deterministically move your pieces, the outcome of an action also involves throwing of the dice, and you can’t predict those.
There’s a certain amount of randomness involved for the outcome of dice, and therefore, we call this stochastic.