I often read about really rich people with billions of dollars, and I'd like to know if they have, for example, just a big part of their wealth in shares of their company or they have lots of wealth in not productive activities?
Wealthy individuals have invested most of their money.
One of the biggest reasons for this is inflation. Most countries, especially those in the West, have a small, positive rate of inflation. Inflation is why a dollar when our grandparents were children was worth much more than a dollar is worth today.
If the "rich" simply stored their money in their mattresses or personal vaults, their real wealth would slowly decrease due to inflation.
Another reason that these individuals invest their money is to continue building more wealth. There is a remote chance that the artist on the street will become the next Rembrandt and their paintings will be worth millions. But chances are more likely that a specific business will do well or that the economy will rebound (increasing the value of their stock and increasing the investor's net worth).