I think of Old Money in the sense of stuff that isn't showy, but when you handle the items or see them up close, you know instantly they are premium items.
Clothes are the classic example. They don't have gaudy logos or anything like that to call attention to them. But they're stuff that you could hand down. Real quality wool, cashmere, the buttons themselves are premium, that kind of thing.
Cars again are more upscale touring types, not sports cars. The richest guy I've known drove a Hyundai Santa Fe. He spent his money on houses and fancy travel and his car was just for getting around.
New money is the showy and usually overpriced stuff covered in logos.
Simplest way to think of it is New Money is for newly rich people that feel the need to wave it around they've made it big. Old Money knows blowing it to impress people is stupid. You buy stuff that enhances your life and pampers you.
We live in a relatively low cost of living area and make decent money. We could pull off New Money if either of us cared about that. We cannot afford anything I'd consider Old Money. That's a whole different world.