Look into dead reckoning vs lock step for networking. Lockstep requires determinism at the simulation layer, dead reckoning can be much more tolerant of differences and latency. Quake and most action games tend to be dead reckoning (with more modern ones including time rewind and some other neat tricks).
Very common that replay/demo uses the network stack of it's present in a game.
An interesting thing about the a lockstep solution which only considers inputs is that any RNG required in the game must be generated from the input history somehow. This could lead to players being able to manipulate their luck with extremely precise inputs.
I used to be a professional sailor, and love finding nautical terminology in programming. At sea dead reckoning is navigating using the speed and direction of the ship, and adding tide and wind to calculate a fix based on the last known position. The term dates back to the 1600s.
It is fun to point at a chart and confidently state “We’re here! I reckon...”