I went to a school that was (and still is) a boarding school, but not a private or fee paying school and I wasn't a boarder. And for all that, very socially mixed in attendance and outcome.
My husband was privately schooled and between going to college in a city and meeting him I definitely noticed the social divide between us rural kids and the city class system (as you would see it through the Pres boys, CBC, Scoil Mhuire and Aloysius in Cork and the Dublin ones -Loreto, Gonzaga, Belvedere, Mounties). I was nearly in my 20s before I really noticed the class system in Ireland but I figured it really is more to be found in urban centres.
I now work in a role in the UK where a large amount of my colleagues are privately schooled and oxbridge educated, and it's very othering - you don't notice as much until you realise that the most prized graduate schemes have spaces for your Duke of Edinburgh's and your extra curricular achievements when nothing like that ever formed a part of a rural Irish education unless your parents were knowledgeable and motivated enough to seek it out for you. Which as mine were generationally farmers, they mostly didn't even know about let alone think would be possible for their child to do - "it was far from such and such you were reared". So I went from thinking class didn't exist, to didn't matter that much except to city kids, to having it be a huge chasm between me and my colleagues in London.
I notice it even more now the kids are in school. We moved to the best area near the best schools that we could afford to do - because postcode differences matter here for the school catchment - and now we are siloed in a suburb of middle class professionals who are just like us, who are our age and education level and in professional jobs just like ours. I never meet or interact with someone from a different social class much because between work and the house/school, I don't go anywhere.
I tried to explain it once to my extended family (her a local solicitor, him a builder) but I didn't do it very well and I don't think they really got it either.