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.
Very common that replay/demo uses the network stack of it's present in a game.