There is actually no difference between BJJ and GJJ.
BJJ came from Martial Arts that was actually used by Samurai. When the Samurai were replaced by Modern Age Technology, the Samurai had no other specialty so alot of them began teaching. That is where you get alot of the Martial Arts you see today. Jiu-Jitsu was one of those. And among the Teachers, one thought that Jiu-Jitsu was not being tought in its entirety by the other Ex-Samurai. He wanted to teach the complete art of Jiu-Jitsu, not just the watered down Martial Arts being taught to the English and the Americans.
So he started up a School and began teaching. It wasn't long after he opened up his school that he was politically exiled and he moved to Brazil. While in Brazil, he was hired by Gastao Gracie to perform his Martial Arts in his Circus. During all of this, Gastao Gracie offered him and his family a home on land, in exchange for him teaching his oldest son Carlos Gracie this Art of Martial Arts.
Carlos Gracie passed on what he learned to his 3 Brothers, Oswaldo, Gastao Jr, and George. Gastao's youngest son,
Helio was too young and sick at the time to go through training. Although he was sick, he watched his brothers and learned it.
Helio Gracie is who is commonly refered to as the creator of Brazilian Jiu-Jitsu. Although some say it was Carlos Gracie that taught Helio.
Helio is the father of Royce Gracie (The UFC Fighter and Champion) as well as many other children that all teach BJJ.
On a side note. Helio Gracie Has only lost 2 fights in his entire life. The first was against a man named Masahiko Kimura (The Kimura is named after him) when he was 38yrs old. The second was against a man named Valdemar Santana. Valdemar weighed over 100lbs more than Helio. The fight lasted 3hrs and 42mins and Helio was 42yrs Old.
He then went on to beat Valdomiro dos Santos Ferreira at the Age of 54yrs old. Valdomiro was concidered the most dangerious man alive at that time.
Helio's son, Rorion found the UFC. He created it, as a way to demonstrate there familys Martial Arts skills as it pertains to actual combat. Where size doesn't matter, time limits didnt matter, the only goal was to make someone submit or be knocked out. Royce Gracie fought for the Gracie Family during the first 3 UFC Events. And won 2 of them. The 3rd he had to withdrawl from the championship fight because of dehydration.
Doubt many will read this all, but I think its pretty cool that the US Army basically teaches our soldiers how to be a Samuari. So I enjoy all the history behind it :)
http://en.wikipedia.org/wiki/Brazilian_Jiu-Jitsu