Big game engines all have a physics engine whose job is to resolve forces, collisions and constraints efficiently. I think the majority of modern games use a physics engine to some extent. Nevertheless, I have noticed that it is not uncommon for developers to implement features using a "kinematic simulation" instead of a "physics simulation" especially in multiplayer environments. Using the example of a car simulation to clarify these terms a bit more (since I don't think there is standard terminology).
Kinematic Simulation: Collect all the forces (suspension force, gravity, engine force etc). Calculate (and store) the acceleration, velocity, new position etc. Set the location and rotation outside the physics engine (which still handles collisions and motion of objects not related to the car).
Physics Simulation: Collect all the forces add them to the car and let the physics engine resolve what happens.
Is there something that makes client prediction/corrections easier in the kinematic version than the physics version?
Unreals character movement component would be a specific, concrete and very common example. AFAIK while the physics engine is still used for checking for collisions the character itself doesn't simulate physics via the engine but forces are instead added to the movement component which runs its own simulation.