If FPSs are in the player's shoes and TPSs are from behind, let us talk about shooters where the perspective is from above, or top-down. Think of these types of shooters as played from a birds-eye perspective. Many arcade games feature top-down shooters, such as Asteroids and Space Invaders (pictured here):

As you can see, the style of shooter all depends on the perspective of the camera, at least as far as our examples go. There are many sub-genres of shooters (for example survival, rail, light gun, tactical, and so on). All of these would require a whole chapter or even book to discuss, so I encourage you to explore them to deepen your own knowledge.