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A supplementary question - if you enrol at an American college that has such a society, do you automatically become a member of the Greek society? Or do you have to apply to join (and if so, is your application ever rejected)? Or is it strictly invitation-only, restricted to the “right sort” of people? Or do different societies impose different membership rules?
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Good lord, no, you don’t automatically become a member. You have to apply during what’s called “Rush Week” which is when the sororities/fraternities “rush” – i.e., pursue – the girls/guys they want to encourage to join their sorority/fraternaty, although it’s AFAIK really more of a process the other way – the girl or guy indicates interest in the S/F they want to attend. Members have to be voted in, and once in are usually subject to “initiations” that may include hazing – stupid, embarrassing, sometimes dangerous stunts. Hazing is pretty severely frowned on by most colleges/universities these days, but it still happens.
Applying members are AFAIK (not being a Greek or former Greek) voted in or out by the existing S/F members (“sisters” or “brothers”). They used to vote by placing marbles in a box; white marbles meant “yes,” black marbles meant “no” – one black marble and the applicant was rejected – hence the term, “blackballed.”
The old established S/F tend to be racially segregated. They give some lip service to seeking diversity, but black S/F arose as a direct result of the fact that blacks were not accepted at white S/F. (And since S/F are private organizations, with members chosen “secretly” and one vote enough to disqualify a candidate, there’s a fat lot universities can do to prevent this continuing de facto segregation of many larger, older S/F.) There are some newer S/F that are intentionally more inclusive and less cliquey than the older ones. Ironically (if appropriately IMO) black S/F now function more in the way that S/F were intended to function: members support each other in school and beyond, and contacts from the S/F can be of real value when starting out in the working world. White S/F tend to be more purely social.
There is a certain type of student (of which I must admit I was one) that can be disdainful of the Greek system. Where I went to school, the fraternity guys were jocks and meatheads, very hard partyers, and the sorority girls were pretty but stupid and sometimes easy. There also was IME a distinction between the respect fraternities got and the respect (or lack thereof) sororities got. A guy in a fraternity could still be a good student and a good guy, but sorority girls were by default considered shallow and not too bright My dad was in a fraternity and I dated guys in fraternities, but I would never in a million years have rushed a sorority.
Again, this is the opinion of someone who (a) doesn’t really respect the Greek system and (b) never participated in it at all, beyond dating into it and going to a lot of parties. I’m sure a person with fond memories of going Greek will tell you all the ways I’m full of shit.