Dfference between gracie jiu jitsu and brazlian jiu jitsu?

Largely use of the name "Gracie" as a trademark and the type of emphasis the names stand for. Brazilian jiujitsu IS from the Gracies so the names are synonymous. However, over time and various schools of development (and lots of business bickering) the name Gracie Jiujitsu became wholly owned and trademarked by Rorion Gracie. As a result, while the fighting style is the same, the names represent slight differences in approach. Gracie Jiujitsu is still holds the approach toward self-defense while the more generic term of Brazilian Jiujitsu nowadays emphasizes more of the sport fighting aspect.