Jiujitsu was never a martial art as an organized style. It is originally a term for the soft skill techniques. It was not until the Japanese traditional arts came to the Americas that Jiujitsu became a martial art's name as in the instance of "Brazilian Jiu jitsu". Before then there existed no Jujutsu/Jujitsu schools in Japan.
Brazilian Jiujitsu is a derivation of Judo, and not such a direct link to Japanese Jiujitsu. The derivation from Judo to BJJ was originally done by Helio Gracie, to accommodate his smaller size.
Since then, many practitioners have made various adaptations to Brazilian Jiu Jitsu and blended with other martial arts.