Everyone here is right...your choice. Ju jitsu students do compete with judo students at judo tournaments. But not usually the other way around. Jujitsu students initially have a broader knowledge of chokes and locks. Judo students don't have a knowledge of locks beyond arm locks and they tend to get creamed by leg and wrist locks. Jujitsu students study judo to learn better control in their matwork and throws...Jujitsu really doesn't study pinning and throws the way judo does. To be a well rounded judo player you need to be equally effective in standing and matwork, not so for jujitsu students.
Judo came from JJ. BJJ came from judo. So, really, what came first? One of Kano's students went to Brazil, married and stayed; but, didn't have the rank to formally teach judo. So, he called what he taught jujitsu. Kano studied and mastered multiple schools of jujitsu, but didn't like the fact that students got injured all the time. So he simplified and streamlined techniques and eliminated the dangerous and ineffective ones and called it judo. (check out the most recent biography on Kano).