AB, ASL is no different than any other language on earth. They all have different words to say the same thing.
While ASL isn't based on English grammar, its signs are based on English words, and the history of English has causes it to assimilate many languages until it has more words than any other tongue on earth.
Until fairly recently, deaf people were more or less isolated into smaller groups, and those groups develop their own styles of sign, just like folks in Tea Neck, New Jersey, develop their own speech patterns which are different from people in Bastrop, Louisiana, which are different from those in Spokane, Washingtin.
I hope this helps answer some of your concerns.
