Paul, if I may.
Generally speaking, there are social fraternities, professional fraternities, service fraternities. Oh, and honorary fraternities. (or sororities obviously). Still, like the phrase members of greek orgs (those named with greek letters) use goes: "No matter what the letter we're all Greek together".
Professional fraternities are usually where the international fraternity has an orient toward one professional area/major over another e.g. business/law/dentistry/psychology etc. They are usually members of the PFA (Professional Fraternity Assoc.) These are always co-ed (mixed) orgs. So let's say for example there were at your campus multiple professional orgs. You'd probably choose AKPsi as it's less likely they would have two professional (business in this case) fraternities at the same university; although not unheard of (if they did you might choose the one you thought best for you based on programming, size, members etc). The other professional orgs would be catering for other areas such as say Dentistry, Music etc. Very often also members "find their place" in such groups when they
don't necesarily have any desire to work in that field too but *do* have an interest in the underlying ideals of that organisation, do want to be a part of and take advantage of the groups activities (e.g. are interested in the philanthropies that come with it) and benefits (academic encouragement, supportive friends, community service opportunities, professional events etc); never hurts to have people with different interests to keep your group from being too stuffy too and all sorts of people can make great members of an org and get lots out of it themselves.
Social fraternities and sororities are single sex orgs ('Title IX' part of the US Education Act (?) required single-sex professional fraternities to go co-ed and allowed student groups designated as "social" to 'discriminate' for membership on grounds of gender. i.e be all male/all female), their members bond through constant social interaction and pursuit of the ideals and motto etc of that organisation (e.g. compassion, integrity, being a True Gentleman (SAE) etc). Choosing between different social fraternities... prospective members look into the ones at their campus and see which ideals appeal to them, what's offered e.g. some offer structured leadership programs to progress through, see how they fit in with the members of that chapter etc, and generally see how the activities of that group appeal to them Paul. Broadly speaking. Ditto sororities. During recruitment aka rush, interested students will usually have a chance to meet all the groups, there might be interest meetings, maybe take part in some activities with them etc and get to learn all about the group (NPC groups have sets of rules for the 'formal rush' process involving meeting all of the groups, whittling choices down etc). International social sororities are members of the umbrella body NPC, for fraternities it is the NIC. Then, the NPHC is for the historically black fraternities and sororities; they are set up as service organisations with a predominant focus on that and also social ties. There are also Latin-American social orgs (NALFO), locals etc etc.
Service orgs such as APO (Alpha Phi Omega) have as their fundamental role community service and philanthropies. This is not to suggest they don't have lots of social activities, academics etc (or that other types of group don't have community service programs). Just that overall they have that focus.
There'll be different sized groups, different groups. Often prospective members find they feel they fit in with one place more than the next, whatever type of group that might be. Like the Christian Morgenstern quote - Home is not where you live but where they understand you.
Honoraries I believe are usually mixed too; entry into these is via say invite based on a high GPA (Grade Point Average), academic success etc.
Hope that helps a little.