Shooter, is a genre of games.
FPS, Rail Shooter, Third Person Shooter etc. are all sub-genres, or whatever you wish to call them. It doesn't mean saying "shooter" is less correct than saying "FPS". FPS is simply more accurate.
For eg.
Cannibal Corpse. An accurate description is Death Metal. A less accurate description is Heavy Metal. Last of all you could simply call it music. Am I wrong if I just say they play music?
FPS, Rail Shooter, Third Person Shooter etc. are all sub-genres, or whatever you wish to call them. It doesn't mean saying "shooter" is less correct than saying "FPS". FPS is simply more accurate.
For eg.
Cannibal Corpse. An accurate description is Death Metal. A less accurate description is Heavy Metal. Last of all you could simply call it music. Am I wrong if I just say they play music?