For a long time class in the US mostly, if not entirely, meant wealth/income. Sure there were some old money blue bloods running around, but not *a lot* of them. I've noticed that a more UK-ish
concept of class creeping in, which is something like "unless your grandfather was a titled large landowner, you get to claim to be 'working class.'" Everybody but the multigenerational superrich are just humble folk.
Practically every UK politician (Labour, anyway) claims to have "working class roots" which generally means their grandfather owned a factory and was not the 7th Earl of whereever.
I think the US equivalent, in Congress anyway, is being the heir to the family car dealership empire and claiming your summer job "sweeping up" means you have deep hard work experience.