| No, they are not mechanically connected, since the two switches can be | switched in the on or off position independently. However, unless they | are both switched on, power isn't supplied. Likewise, unless they are | both switched off, power isn't turned off.
Your statement is self-contradictory. You are saying in one part that one is on and one is off, that power isn't supplied, and in another part are saying that power isn't turned off. It's either on or off, or maybe some weird voltage.
So let's go over this in detail. And this is what I would examine if I were there diagnosing this for you:
Label these breakers for this purpose as A and B. The box should have them numbered, so for consistency, make A be the lower number and B be the higher number. Do this test with all other breakers ON that would normally be on.
- If A is off and B is off, is the power to that area on or off?
- If A is off and B is on, is the power to that area on or off?
- If A is on and B is off, is the power to that area on or off?
- If A is on and B is on, is the power to that area on or off?
Now repeat the test, but this time with all other breakers OFF, except the main would be ON.
- If A is off and B is off, is the power to that area on or off?
- If A is off and B is on, is the power to that area on or off?
- If A is on and B is off, is the power to that area on or off?
- If A is on and B is on, is the power to that area on or off?
- What actual position numbers are breakers A and B in? How many breakers and breaker spaces (give both numbers whether different or the same) are between them (0 for immediately adjacent)?
Turn all breakers off, including the main breaker, and any breaker or switch you might have feeding this panel. Remove the front and find the wires leading to the two suspect breakers. Examine them very carefully.
- Does each breaker have exactly one wire, or more than one wire?
- What color wire(s) go to breaker A?
- What color wire(s) go to breaker B?
Follow the wires back and see if you can find if the wires join a common cabling, like a single Romex. If so, look at the white wire that cabling has, as well as the bare or green wire, and trace them to where they are attached. Are they in fact attached properly and tightly.
If the wires for these breakers go to separate cabling, please report this fact the best you can. In this case, leave these breakers off, put the panel back together, and restore power except for these two. Then example every receptacle and light and take an inventory of exactly everything that is without power. If you have plenty of time, you might want to open those boxes and see if you can figure out where the separate cabling joins back together, You may have what is known as a "ring circuit", which is usually not compliant with NEC code in the US (and with 2 separate breakers, definitely is not compliant). Or you maybe have some (probably miswired) shared neutral "home run" circuit.
Absolute clarity and complete detail is required for us to figure out what you might actually have. The number of possible ways to miswire circuits is astronomical. Guessing is usually futile. Assumptions can get people hurt or killed.
Tell us where (city, state) you live. Maybe someone here happens to live close to you.