This is so funny because rust has one of the worst cheating situations and majority of their players are windows users, and theres lots of games that have anticheat that allows linux and have notably less significant cheating problems like marvel rivals. in reality rust doesn't take cheating very seriously because if they did they would have more server side software that detects illegitimate behaviour like tons of other games do successfully...... even most popular Minecraft servers have better functioning anti cheat that is completely server side than rust has while getting kernel access to your pc. its pathetic and lazy development tbh and this entire post from them reads like such extreme cope....
For the vast majority of games, it’s in between, because the latency if you waited for the server every frame you moved would be way too much.
It’s something like you have a local model of where everything is, and send updates to the server of where your local model says your character (and whatever else your inputs affect) are. The server receives that data, potentially validates it (server side anti cheat checking that your movement makes sense, similar to the OP post, for example), and then forwards that info to all players. The client side positions of everything are updated based on that info. Usually some interpolation is added to make things move more smoothly.