What is the difference between a flat fee and a fixed-fee?

Can you please clarify the difference between a flat fee and a fixed-fee for me? I've heard both terms used interchangeably, but I'm not sure if they mean the same thing. Is there a specific scenario where one would be more appropriate than the other? Additionally, do they both involve a predetermined amount of money that doesn't change, regardless of the services provided or the time spent on them?