Yes, each country has its own Deaf Culture and consequentially, its own Sign Language.

Logically looking at the given, this would be a natural consequence, for instance Spanish Deaf living in Spain and being influenced by the old historical culture of the hearing Spain, with its unique gastronomy, language, etc. Sign languages formerly established and regulated are LSF (langue des signes franaise), BSL (British Sign Language), GSL (German Sign Language) and many others, but none can claim to be the origin of sign language.

To explain some more, if we look at the alphabet, most of the letters that forms a word, should have some uniformity in its outcome as for instance if we, in all English and related cultures "spell" water, we will start with a "W". In most Latin influenced countries, water is translated to aqua and thus starts with an "A". Deaf cultures are related to the cultures of a specific region and thus as languages differs to this great extent so does sign language differs all over the spectrum.

In Canada and the United States of America, ASL (American Sign Language) is generally preferred as the vehicle of communication for the Hard of Hearing and the Deaf alike. SEE (Signed Exact English) and BSL (British Signed Language) to a lesser degree are also used by some, as they perceived it to be more in line with English speech.