I've heard that Carlos Gracie once said something along the lines of, "Judo and BJJ should in theory be the same, but the Japanese forgot how to do submissions and the Brazilians are too lazy to practice their throws."

In terms of BJJ vs. JJ/judo, I believe BJJ is referred to because the ruleset, terminology, goals, and overall culture changed after the Gracies took what Maeda taught them and changed it.

Generally people call what they're doing BJJ because JJ could mean a huge number of ryus for Japanese JJ or even something broader like American JJ, all of which have different sets of techniques and methods of training, so the distinction of particular styles of JJ is important when describing what one trains. In a large part, there's a huge respect if one were to have a black belt in BJJ because that is a known constant in terms of dedication, knowledge, and ability to tap fools out. But if one were to say they train just JJ, nobody would know exactly what that means and what their actual fighting ability is. So I believe many Japanese fighters would say what they're doing when they're fighting is jiu-jitsu, but the martial art/style they train is BJJ. Make sense?