Being taken care of.. Being well off... Never having to worry about buying anything. As in you can buy whatever you want.
Being more well-off than your peers. As in having a lot more money than they do. Being well-ahead of them financially.
For instance Bill Gates is a lot wealthier than all the people his age, he's rich.
Your boyfriend gave you all that money?
Damn, You're rich.
Look at that CEO, He's rich.
Look at that model, she's rich.