There is definately a difference. The concept of Graduate chapters as far as I know only exists in the Noble Nine and those groups aspiring to join them in the NPHC. There are two *large* rights given to graduate chapters that are not given to ALpha Phi Omega alumni associations.
1) To make new brothers (sisters). In all of the NPHC, Graduate chapters have equal ability to make new brothers with, I believe, the only difference being that to become part of a graduate chapter, you need to already have a degree from a 4-year institution.
2) To vote at the National Convention. At the very least, for Alpha Kappa Alpha and Kappa Alpha Psi (I think), the graduate chapters have more votes in convention than do the undergraduate chapters. It is only in the last 10 years that the fraternity has allowed an alumni vote for each region and at the most significant re-write of Alpha Phi Omega's organization (1967 con-con) alumni were not even allowed any vote (including the national president!)
Some groups do try. The fraternity has had to take action against alumni associations who have tried to make new brothers. Right now it is *much* easier to make an alumni association than to make a chapter, I don't know how many alumni associations would be willing to put themselves through the types of requirements that new chapters have to. As far as I know all graduate chapters are based entirely on location, so all of the groups based on being alumni of the same chapter would have to go.
I'll be happy to share more opinions on the relationship, but I think this is enough for now.
Randolph Finder