No , the two are seperate teams .

There is a never ending list of X-men. The list is far too big to put here, but you can find a full list at wikipedia.org and marvel.wikia.com.

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Many of the X-men have belonged to several different teams all at the same time. The X-men are a main team, while they also have several associated teams such as X-Factor, Excalibur, and X-Force. They have also been known to team up with the Starjammers and even the Avengers, borrowing members from each other and such. Wolverine is famous for belonging to several different teams at once and it has become a running gag.

Storm has been a team leader for various X-Men teams. This happened for the first time in 1980's Uncanny X-Men #139. Other examples would include X-Men Gold Team (Cyclops led Blue Team) in the 90's and X-Treme X-Men in the 00's.