There’s a world of difference in disposition between new money and old money, in my experience, and flashy-car-and-expensive-jewelry rich is decidedly new money. Families with generational wealth tend to be more discreet about it, and often have a “noblesse obligee” mentally about how they engage with the world. New money’s much more likely to pull the “don’t you know who I am?!” card.
Similarly, there’s a split between working class folks who know the score and recognize that they’re all in it together with the guy behind the counter, and the sort of temporarily-embarrassed millionaires who have themselves convinced they’re better than they are.