The concept of Class as used by Karl Marx had a different meaning. Middle Class had no meaning to Marx. In the last century, most people were in one class or the other all of their life, and the Capitalist were richer. Today things are much more muddled. While there are certainly exceptions, the more normal pattern today is that most people are a little of both.
People usually start out as workers.
But as they get older, they are saving for retirement.