Put simply, rich people have money; but they do not necessarily know money. To be rich is to earn a lot of money or own a lot of things, but also have a high cost of living or a number of expenses which makes this money less sustainable.
While not all rich people are wealthy; all wealthy people are rich. The difference is that wealthy people are able to control and manage their money in order to create a sustainable lifestyle. They can enjoy a rich life without a time limit.