They are obviously related, but it is a very loose correlation. If a billionaire (who does not pay me) gives me an order I will laugh in his face. If a traffic cop gives me an order, I will comply.
> (who does not pay me)
You're answering a comment saying money is power by saying that it isn't if it's not used?
Even if the billionaire doesn't pay you, they can pay someone else to force you to do what they want.
This doesn't mean money has no power over you.
Perhaps the billionaire can't buy your willingness to do something, but they can very much affect the material world around you, and therefore, you.
If you rent they can probably find a way to kick you out of your apartment. If someone around you _is_ willing to take an order, influencing what people around you do very much influences you. If they want something from you, and you're not willing to sell it, there will be people willing to steal it, etc.
Money very much is proxy of power. Perhaps not everything can be bought, sure. But money gives you operational range to attempt to impose your will when it doesn't.