That's true for the entire language but, like a lot of other languages, there is significant overlap. For example, the American in American Sign Language means North American; it is the predominant manual language in Canada and the United States and has fairly wide acceptance in Mexico.

ASL is based on LSF, or French Sign Language, because of a long history (more or less involving the person with the last name Gallaudet) but the main point is that a lot of sign languages descend from LSF. Much like how someone who only knows English can go to Germany or France or Italy and make out some of the basic words, the overlap between LSF descendants is pretty good for basic or everyday use. I'm semi-fluent in ASL and I've successfully communicated with people who use Irish Sign Language and German Sign Language (DGS).

The big stand-out is British Sign Language, or BSL. BSL's manual alphabet and root signs are dramatically different from LSF. (Since a lot of ASL words are initialized motions, like taking the first letter of the English or French word and using that handshape sign in a motion, BSL doesn't translate as quickly.)