Wealth gives everyone power. The difference is that when most people want to excersise the power their wealth gives them, they do so by exchanging money for goods or services. For instance, I can influence a plumber to fix my toilet by paying them.

Rich people do that too, but with a proportionally tiny amount of money. Most of their influence comes from the fact that they simply own stuff. They don't need to spend money to pay for entities they own to do what they want. If you own a voting stake in a company, you do not need to spend that stake to influence the company.