Chess Engine Random Tactic Variance

If a specific chess engine (such as stockfish) plays against itself does it always play the same game or are there random variations built into its decisions?

I have seen stats for different chess engines playing each other where the outcome varies in each game but if a chess engine plays an identical copy of itself are the moves always identical or does it roll the dice a little with opening moves?

I think it depends on the engine

I'm very interested in this question and would love to know more about how randomness fits into contemporary chess engines. I have played around with chess games on my mobile and, for example, most respond to E2-E4 with e7-e5, but sometimes its c7-c6 if I close the app and open it again (rebooting the engine). Are there random variables locked in that stay in place during the session?