Call of Juarez on Steam
store.steampowered.com
Call of Juarez is an epic adventure western themed FPS game. The player alternately assumes the roles of two distinct, antagonistic characters: a sneaking fugitive Billy and his hunter the reverend Ray.

Is there a name for games where you shoot but don’t control the movement?

An example would be Call of Juarez

Possibly there is a Steam filter with these kinds of games?