Re: Gracie Jiu Jitsu & BJJ
Gracie Jiu Jitsu refers to the Gracie family style, it is the standard in Brazil. When others began to branch off from the Gracie family, and/or non-Gracie family began to teach the "Gracie style", or their own version of it they could not use the name Gracie, so BJJ became the more generic umbrella term for Brazilian Jiu Jitsu.
BJJ includes Gracie JJ as well as other styles of JJ, but nearly all the JJ that originates in Brazil is either directly derived from or influenced by Gracie JJ.
Specifically, Gracie JJ as a trademark refers to the art as systematically taught by Helio Gracie and his sons. There were other Gracie's - perhaps most notably the line from Carlos Gracie who was Helio's brother.