So I want to know how this type of camera is called?
so there is a way to make the camera smoother. so when you move your mouse to a location on the screen in first person, the camera eases in and not goes linear path.
here is a video explaining what I mean: camera video
It would probably be done using linear interpolation, which takes that linear path that the camera normally uses, and curves the linear path to make the camera move in a smoother way.
There is also someone else who asked this sort of question, so hopefully this helps
My way of doing it is making the camera scriptable, lock onto your head, and somehow make it moveable by using your mouse, and instead tweening it to a position.