Shoot wrestling is related to catch. A "shoot" is opposite of a "work" in pro wrestling terms, in that it is a "real match" without a predetermined outcome.
Shoot wrestling / shoot fighting came up as a term when organizations in Japan like Shooto and Pancrase started doing more real matches (early MMA)
Anyways, Catch wrestling is what modern wrestling evolved from. The Olympic styles dropped the submissions, the pro stuff turned to all works. But the basic concept was you win if you pin your opponent or get them to submit. A lot of the times chokes where not allowed, and there was a greater emphasis on leg attacks then BJJ. Submissions where often used as a means to force a person to roll to their back so that they could be pinned as well.
BJJ focuses more on submission, but removes a lot of leg attacks and wears a gi. It also has a point structure which takes a lot of the emphasis away from takedowns and allows a lot more fighting off your back (guard).
They are reasonably similar, and there was a fair bit of influence each had on the other. The differences are more in emphasis then content if that makes sense.