Your definition of wealth is broken. A car is wealth. It may be a depreciating asset, but it is still wealth. It has value in its materials. It has value in its construction. It has value in its utility. A car most certainly can make money.
Wealth consists of all things that have value. Shares in a company are wealth. Dollars in your pocket are wealth. A house is wealth. A coal mine is wealth.
No, that's an asset. A car is wealth, and could be either an asset or a liability, depending on the car and what you do with it, but it's still wealth.
Wealth is owning things that can make money, not things that are money or that were bought with money.