Yes very possible the FP is wired to the other breaker labeled general. In fact From what you describe Id say it’s definitely wired to the general labeled breaker.
How many wires are coming into the general breaker? A bunch?
Also trip the FP breaker and see what doesn’t work.
(Have you actually opened up the panel and see a wire to the FP breaker?)
If you aren’t very familiar with residential electrical, you’d be surprised what you might find out, depending on how hungover the electrician was that day….lol