...but you can stay working class if you create a $Bn oil company.
...
In the USA, most people use "class" as a shorthand for "income" or "wealth". In Europe, parts of Canada, and many other parts of the world the concept of "class" refers to a subculture.
For example: if your title includes "Duke of..." or "Count of..." then you're a member of the hereditary nobility, and there's a bunch of baggage that goes along with that. Wealth is characteristic of the subculture, and there have been times when conspicuous consumption was part of that subculture. But at the very same time, people were often flat broke (due to bad investments or too much of that conspicuous consumption). They didn't stop being lords and ladies just because they were living in a rented room instead of a palace.
The USA and Canada don't have hereditary nobility, but there are definitely old families and socially prominent families, not all of whom are as obnoxiously ostentatious as the ones who run for public office or have their names in the newspaper for doing something stupid. There's social baggage that goes along with it. If you want an unvarnished look at the kind of decisions people make because of class related social baggage, read "The House of Mirth" by Edith Wharton. The culture being described is "high society" New York in the early 1900's, and it's distinct enough from anybody's present culture for the social baggage to be immediately visible as such.
Class has been described as a set of choices and preferences that people have, that are nearly universal ideals within a subculture. My grandmother always said that class is "how you treat people", the emphasis being that people show their class depending on what duties they have to others, how they perform those duties, and whether they need to be compensated for them. I think of class as the social baggage that goes along with the group that you're part of: it makes up so much of a person's perspective and value system that it's invisible unless you're outside it. What "hospitality" should look like, what your responsibilities to family members should be, what manner of belongings you choose (given the resources to obtain them) and your attitude toward education and asset accumulation will all vary depending on your class.
Incidentally, there's no such thing as a "superior" class versus an "inferior" class although it's true that some tend to accumulate more resources. Belonging to a class requires that you believe it to be superior to the others, either by virtue of privilege or by moral superiority. There is such a thing as an alpha/beta role when people of different classes have business or social relationships, but you'd be surprised who generally thinks they're the alpha. Ironically, the countries that have cultures with the greatest emphasis on class tend to be the ones with the most symbiotic approach to the relationship between people who pay for services and people who perform them. The alpha/beta bullying and status games are the most vicious in societies that pride themselves on being "classless".
Anyway, how you're expected to obtain your money and resources will vary depending on what social baggage is attached to the group you were born into and/or raised in.
Does that make sense?