Quote: "But then A story line in an FPS, technically, you are taking on a role, and so would also be a role playing game - where do you really draw the line between those two?"
In most games there is a clear distinction, and it is easy to tell which type it is (although a game may contain elements of many genres). FPS is just a sub-set of Shoot-em-up games. For example, Max Payne is in third person, and is a Shoot-em-up game. If the game was played from a first person perspective, I'd say it would qualify as a FPS, but as it stands, it is not. Morrowind is first person, but it is an RPG, and although you can shoot at enemies with various weapons, the majority of elements in the game are distinctly RPG-esque.
In answer to your question, it is as with everything. When does an embryo become an un-born child (not trying to start a moral debate here!)? There is no line at which an RPG becomes a FPS, or at which a RTS becomes a puzzler, but most games are extreme enough either way for there to be a clear distinction.
