I agree to an extent, "upperclass", "underclass", "middle class", "lower class" and so on are not meaningful ways to describe societal structure, they're mostly arbitrary delineations to group income brackets with similar consumption levels and behaviors.
In the UK class still refers more to traditional social standing (i.e. someone from a bloodline of aristocrats would be considered "upper class" even if they have a measly income and no generational wealth or political status) but in the US this has almost entirely eroded to refer to how much money you make (with even distinctions between "new money" and "old money" evaporating over time). Most countries lie somewhere in between.
Marxists often try to be similarly reductive by saying ownership of "the means of production" is the only class distinction. But even Karl Marx wouldn't have agreed with this strictly binary approach.
If you spend even a few seconds studying the biographies of the top billionaires, it should be obvious that even a small-scale business owner has less in common with them than with the working poor. If there is a single dividing line, I would say it is if money means being able to purchase goods and services, or if it means being able to exert political power.
A billionaire not only has at least a thousand times as much money as someone with a thousand dollars to their name. This level of wealth compounds. Merely having this amount of money readily available not only affords them easy access to credit (and thus additional liquidity) but it also affects other people's (and companies') behavior towards them. Poor people on the other hand have to resort to collective bargaining (e.g. labor/trade unions).