Server authoritative
Also said as Authoritative server, Dedicated server, Client-server
One machine, the server, decides what really happened. Players' machines send only what was pressed and show what they are told.
It is the only reliable defence against many cheats, because a hacked game can only lie to itself. The costs are a server bill and a round trip on everything, which is why it needs prediction to feel good.
Say it
“Clients send inputs and nothing else. The server moves everyone and decides every hit, and it never accepts a position from a client, even a position that seems reasonable.”
Where you’ve seen it
Riot's rule for Valorant is that "a server must never trust a client's view of the world". The first Diablo is the warning: it lacked those defences, and many of its online characters were altered with trainers and editing tools.
Not to be confused with client authoritative
In a client-authoritative game, each machine reports what happened to it, and everyone believes it. It is simple, and a cheater needs only to change the report.