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First-Person Shooter refers to a genre where the camera is at the same place as your eyes: you see (on screen) the scenes just like you'd experience it.

Shoot 'Em Up or shmup games are a subset of shooter games where the player continually moves forward while waves of enemies enter the screen. Both shooting and dodging are critical to advancing. See also Bullet Hell.

TPS or Third Person Shooters are shooter games that have an over the shoulder or behind and above view instead of an eye to eye view.