There really is not any difference. I think they keep the Tip-Off name in deference to it's history. For 40 years or more the Tip-Off Club was the only support group for the basketball program. It was run independent of the university,ran it's own membership,raised it's own money,had it's own checkbook. Sometime in the late 1980's the university thought this was a bad idea. The university and the NCAA wanted institutional controle. In a hostile takeover the Billiken Club was formed and the Tip-Off Club was folded in. I think they keep the name out of respect for some of the former members. It also provides some difference between basketball supporters and the rest of the athletic dept.