From my limited understanding of fraternities and what Sage said, the normal process is that:
1.) Students join fraternity during college
2.) Students who join that fraternity develop a sort of clan/pack mentality where they think of the frat as a second family
3.) Those former students, now alumni, donate to the fraternity for the benefit of future members, so they can have the same experience/togetherness the old members had
4.) To supplement donations, current members of the fraternity also perform activities that help them raise funds. Sage mentioned the HOTs do social work, the Jocks probably get money from the gym in addition to their own locker room since they're probably good advertisement for the gym. The MC outright says the gym probably sponsors them.
DIKs are different because they literally just started a few years ago and all of it was paid for by just Rusty's dad. Prior to the alphas thrashing the place and the MC rallying the DIKs together, all the DIKs do is party without actually working for any of it. Of course, the preps don't really do work, either, because I presume their donations are huge considering the background of their members. But yeah, the money is from old members generally, whereas the DIKs don't have old members. You're right that they're technically both being paid for by parents, but the DIKs are a little different because they're basically ignoring the way things are usually done. This is especially true for Tommy, who's basically mooching off Rusty for most of the ride.
