"How is sign language different in other countries? For example, would the sign for "cat" be different in American than Spain...hence AMERICAN Sign Language"
Possibly, possibly not. ASL is used mostly in Canada and the U.S.
Also, just because English is spoken in Australia, the UK, and lots of other countries, doesn't mean their Sign Language is the same -- each one has their own Sign Language.
Still, when there are international gatherings, I believe Gesturo is used (I don't think it's like Esperanto, but it is intended to be used for those who use lots of different Sign Languages).
This is a really interesting site... (and the guy is very entertaining)
Deaf cultures and Sign Languages of the world