“Lag” does indeed come from network/signal theory and does indeed refer to networking. Been a minute, but I want to say lag is the round trip delay and latency is A to B but don’t quote me on that.

That said? Nobody cared. “Lag” was always the time between action and response. Some of that might be input delay. Some of that might be display delay (which has always been over-exaggerated but…). And a lot of that really was network delay. These days it tends to be more rendering/logic delay because people who are playing on shitty internet connections know it.