For rich people who want to uphold the status quo these two things are identical, sadly.

Both are relative terms so they can be the same or different depending on who defines them. Nearly everyone that works in the US is rich by worldwide standards, so it's not clear that a lack of billionaires for example would make things better. Sans Amazon, Apple or Google, would the US be better off? I'm not convinced.

Most people's definition of rich is "one dollar more than I have". Just look at laptop class's hate on the 1 percenters - which actually includes them.