An economist would say that the upper class, whether European, British, or American, lives principally on inherited money. The upper middle class or bourgeoisie was historically defined as the people who were rich, maybe in some cases richer than the upper class, but they earned all or most of their money. This would include successful physicians, attorneys, and business people, those who might have inherited some money but had to work hard and acquire quite a bit of education in order to be successful. So most of the rich people who are visible to us tend to be members of the upper middle class. Most people are unaware that there is an upper class in this country because its members are very reticent and private, for the most part.
Of course, class is not really a question of how much money you have, but how you spend whatever you have, what your tastes, values, and aspirations are, how you live, and how you conduct yourself. Our Founding Fathers may have done away with a hereditary nobility but they couldn’t stamp out human ambition.
With all due respect, I question this. The aristocracy, et. al. are the "upper class" you spoke of,does not gain statue from inherited wealth -- more particularly from the mid-19th century onwards. Originally aristocracy was based on feudalism, and with it lineage; it maintained by land, specifically renting land for agriculture. Today, it's pretty much based on nothing...or anything.
The haute bourgeoisie is the upper middle class. The doctors, dentist, lawyers, owners of large companies, etc. In short, folks who work with their heads more than their hand. The petite bourgeois are the middle-middle class. They work equally with both head and hands. The proletariat work chiefly with their hands and, well, don't much think about work when that 5 o'clock whistle blows, esp. on a Friday afternoon.