Does Islam really exists?

This is something I just realized, watching on CNN how Suni and Shia Muslims masacre each other. It comes down to two separate hospital systems in the same capital city, one Shia and one Suni, one supported by government and one not. To get to the wrong hospital might be signing your death warrant. Yes.

Remember, all monoteistic religions are unanimouse in that there is exactly one God, and naming him differently doesn't makes him different. So we have Shia and Suni that both believe in god named Allah, but if we leave the name alone, there is probably more in common between Buddists and Hindus then between Shia and Suni.

Of course, lets not forget that Shia and Suni are not the only ones. There are many other different "Muslims" in the world. For example Pushtun Muslims still keep millenia old Jewish traditions. Sufi "Muslims" came before Islam, and are very different from both Shia or Suni in their beliefs (although Suni consider them as their own). Then there are the Ahmadiyya "Muslims", who are still very different from other "Muslims", and remind more the Bahai sect then anything else, who are not considered Muslim at all, although were initially formed as an extension of Islam.

Of course, this list is far from complete, but you get the picture. Who can be considered true Muslim? I can say from personal expirience that Muslims themselves cannot agree on this. So is there such a religion?