Neither thing is necessarily true and, in the main, it isn’t. It depends on what a person’s wealth is composed of. If a person’s wealth is in municipal bonds, he won’t pay taxes on that income unless he hits the AMT.
If his wealth is in stocks and his income is totally from that, he will pay less tax on dividends and capital gains than the median tax rate, again unless he hits the AMT. A lot of elderly peoples’ income is largely from this source, or bonds.
If his wealth is in farming or ranching, it’s mostly in the land, equipment and livestock. He pays ordinary income tax rates on his net income. The only capital gain he’s likely to get would be for breeding stock and then only if it isn’t his main business to sell breeding stock. He also has to pay the payroll tax at DOUBLE the rate an employee pays. He will pay more taxes than a person of no wealth but who has the same income.
Small business peoples’ income is mostly taxed at regular rates, and they, too, pay DOUBLE the payroll tax rate people pay who are not self-employed. He will pay more taxes than a person of no wealth but who has the same income.
Small business people and farmers “buy their wealth”, so to speak, with after-tax dollars.
Wage earners, on the other hand, “buy their wealth” with before-tax dollars. Government workers, of course “buy their wealth” with other peoples’ dollars.
I think a lot of folks don’t understand what “wealth” is, who the “wealthy” are or what “wealth” actually does for anyone.