Yes, your friend is right.
Sign languages can be roughly divided into 2 categories- sign languages that are living languages in their own right (American Sign Language -ASL), and sign languages that are a signed version of a spoken language (Signed English).
ASL has nothing to do with English except that it's used in the US. Linguistically it doesn't follow the same rules as English. Signed English is the same as English, except you use signs instead of sounds.
Mexican sign language (Lenguaje de señas mexicano, Lenguaje de signos mexicano, LSM) is not related to ASL and is unintelligible to ASL signers. There is also another sign language used by the Mayan-speaking community in the Yucatán peninsula, but I can't remember it's name.
There are dozens if not hundreds of other sign languages in other parts of the world.
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If you find something wrong with my Spanish, please correct it!
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