By the conventional terminology (which could admittedly be less ambiguous) "client prediction" is where the client shows the player a locally predicted present

By the conventional terminology (which could admittedly be less ambiguous) "client prediction" is where the client shows the player a locally predicted present game state inferred from stale authoritative information. The client guesses what is actually happening right now based on what it knows was happening some time in the past, as told by prior updates it received from the server. This works if there is a lot of temporal continuity in the game, such as there is when the laws of physics are obeyed. Sources of entropy, like player input, can't be predicted and so that is where inconsistencies will appear. "Lag compensation" is where the server accounts for client latency when making certain authoritative game logic decisions i.e. "did a bullet hit a target y/n"? Essentially, it decouples the when and the where of the event. So a target can be hit by a bullet now but the hit took place where the target was some time in the past. Since that would generally feel ridiculous to the player, it can only be done in very particular situations where the event is mostly entropic and instantaneous, and therefore unpredictable (e.g. a player firing a bullet with infinite velocity) and where the inconsistency is unlikely to be noticed (because you typically aren't paying much attention to where other players are aiming). The lag comp described on that page you linked to is only for player vs NPC, where the NPC is totally predictable and therefor always appears in the same place to all players. If you tried to lag comp a slow moving projectile with player vs player then the projectile would have a curved path, following the target around as they tried to dodge it. It would give a blatant unfair advantage to lagged players. I don't see any lag comp options for light cycles since your only real options for bending the game rules are a) letting players pass through walls/crash into walls that aren't there or b) moving players/walls around retroactively, both of which will appear obvious and unfair.