I suspect that the phrase came from “Rich Dad, Poor Dad”, where the writer explained the benefits…
Memphis Blues

Having listened to all but the most recent episode(it’s on deck for my drive home), this is how I interpreted it — “rich person thinking” is putting the money to work making more money, while “poor person thinking” is buying depreciating or ephemeral goods or services. She talked in an early episode about how her boyfriend (who was raised by parents who both had enough money and were comfortable talking about money) would save or invest excess money he got, where she, who was raised by financially irresponsible parents, would spend it on things or help out her younger sister with bills.