Super Saiya-jin is the name in Japanese, but in that language the "-jin" part is a suffix that is added to a place name to form the word for a person from that place. In other words, it means a person, and it's attached to a word for their nationality, origin, or race. Someone born in USA would be "amerika-jin", and someone from Japan would be "nihon-jin". When Saiya-jin is being stated, it is meaning something like "Saiya person".
In early DBZ fan communities the word was often mistranslated as "Saiyajin" and not "Saiya-jin", and that's how this spread as "SSJ" and not "SS".
That said, everyone is free to use what they are more comfortable with, but I wanted to share that the usage is incorrect. You can ignore the J entirely as even in Japanese they ignore it.
In early DBZ fan communities the word was often mistranslated as "Saiyajin" and not "Saiya-jin", and that's how this spread as "SSJ" and not "SS".
That said, everyone is free to use what they are more comfortable with, but I wanted to share that the usage is incorrect. You can ignore the J entirely as even in Japanese they ignore it.
