Yes one is derived from the other, that is very much true. In fact it was a Japanes master that taught the first Gracie and after only 8 months of teaching he had to return to Japan so he couldnt finish. After that the Gracies began teaching themselves and in fact the Brazilian Jui-Jitsu we know now would have NEVER come into place. It was one of the yonger, much SMALLER, brothers that turned it into the highly technical submitting machine that it is. He was getting tossed around and over powered by his other brothers so he had to adapt what he know to suit him and he did, instead of worrying about power take downs and strikes he concentrated on the technical part of it, how to attack the bodies weakest parts.

Anyway, there are HUGE differences between the 2 arts. Judo was a Samurai art, designed to disarm other Samurai's that had swords or other weapons and to harm them even while they still had on that very tough armor so the hits and throws are extremely powerful and take a bit a strength. Yes, they work off of leverage but mostly off of power to inflict the most damage. Leverage was used as a helping step to gain power into a throw but not as the MAIN component. In BJJ leverage is the primary weapon in almost EVERYTHING taught.