"The demand for money is a demand for wealth." Is this statement true?
If you are talking about “demand for money” as a technical economic term, this statement is not true. The demand for money, as an economic concept, is very different than demand for wealth.
Wealth is something that we all want. Almost everyone in the world wants wealth in almost unlimited quantities. This is because we want the ability to buy whatever we want and the ability to have so much money that we do not have to worry about our futures. But this is not the same thing as the demand for money.
When we have a certain amount of wealth, we do not typically want to hold all of that wealth in money. That is, we do not want to have it all in cash. The reason for that is that cash really does not do much for us unless we want to use it to buy things. If we have excess wealth that we do not need to use to buy things, we are better off putting it in investments that will earn us more money. This is much smarter than simply holding that wealth in the form of cash.
So, the demand for money is the demand for cash (or other liquid forms of money), not the demand for wealth. Our demand for wealth is more or less unlimited. By contrast, we only typically demand enough cash to be able to buy the things we need on a day to day basis. The demand for money is the demand for the cash that we think we will need.