I don't totally understand it, as I don't travel in those circles. However, there are like 100,000 people in the social register. That is pretty closed, which is partly why the children or grandchildren of someone who made a lot of money and married someone not quite at that level would marry British aristocracy. Newport, RI was were New York society had summer homes, so newly wealthy people built spectacular mansions there and had parties for the socialites they wanted to marry their kids to.
I was acquainted with someone who went to a top 50 prep school. She was not in the social register, but her grandparents owned what had been 4 plantations. Her middle name was the surname of a well known colonial governor, and her siblings had middle names of generals they were descended from. She was near the bottom of the class at that school, so I assume they look at background even if you aren't in the register.
I had a cousin who went to a top 10 prep school on a scholarship. I wouldn't want to do that. I had enough trouble at a fancy college with all the prep school types and rich kids who were bought in looking down on me. There was a movie "School Ties" about kids on scholarships at top prep schools, sometimes because they wanted them for an athletic team. They would have them work as waiters serving meals to the other kids as their job for the scholarship.
A friend told me a story about meeting a society type at his mens club to discuss some business. In addition to the high class types there were all sorts of news people from TV, old rock stars etc. They seemed to bring people like that in for connections, information, and so on. There was an article like 30 years ago about a club like that in Washington, which had one Jewish member Henry Kissinger, and a black member who was an Episcopal bishop.
These top prep schools and clubs and so on are financed to a large degree by wealthy people buying their way into them. You can buy your way into a prep school as well as a college, but the normal way to get in is on background for a prep school. By contrast college admissions is supposedly based on academics, but you can buy your way in, and there is preference for prep school types, political connections, etc.
Joseph Kennedy, the father of the president, had been bought into Harvard. He bought his kids into top prep schools. He also was made Ambassador to Britain, partly because he donated a lot of money to Roosevelt''s campaign. Roosevelt also wanted him happy and out of the country, so he wouldn't try to become president, and it maybe got Irish votes. The Ambassadors to glamorous places mostly bought there positions with campaign contributions and maybe money under the table and are mostly nouveau types looking for status. Professional diplomats have to pass a test on history, geography, and so on and know lots of languages, but are also mostly from fancy backgrounds. Background is really important in the foreign service, but not so much in the military any more.
My understanding is that it helps to be social register and good prep school for competitive colleges. The top Ivies take a lot of people from top prep schools who are good academically, but also upper level society, which isn't really viewed like aristocracy in Europe but has status. Top Ivies also are really expensive to buy into, so have really rich students.
Admissions to good prep schools is mostly based on background, but I have heard less so than in Britain. Some Ivies and top LACs take maybe 15% of students on academics, and the rest have hooks. They take some for athletics, some who are from underrepresented ethnic groups or geographical areas, and some with various types of connections or prominent parents or relatives. Then there are a lot of prep school types, but most are sort of bought in.