Nah, I actually had the same question, and Jazzy Jay is an older guy who pioneered the whole turntable scratching/live mixing DJ techniques back in the 70's. He also helped start Def Jam Records. The guy from Fresh Prince is Jazzy Jeff. It's kinda confusing since they just called him Jazz on the show. And they're both DJs. It left me scratching my head for a while too.
hahahahahahah DJ Jazzy Jay, never atually heard of him... I read that he helped on the Fort Minor We Major Mix tape