You can refer to her as anything you want. It's your life.
However, a mistress usually means that she's exclusively yours, you maintain her lifestyle, everything.
AMP workers have regular clients but also deal with a high volume of customers.
But both are sex workers, as are escorts, hookers and providers and companions--my word for them.
Rich guys have mistresses, good for them. But I wouldn't want to get tied down having to take care of one just to get my needs met. It just becomes another committed relationship. I don't envy them.