Allow me to ask why there are sometimes multiple autopilot on/off switches (Command switch)? Are these for different channels, for instance say the captain only wants the A/P to handle pitch and therefore only the elevator channel is turned on?
Think of each switch as an "ON-OFF switch. The difference for the autopilot is that one can use some of it's capability, or all of it.
If three switches are installed, that's for three different autopilots. Generally only one autopilot is in use at a time. For certain operations, such as autoland, more than one autopilot is used. Certain things must take place during an approach to land, or one or more autopilots will be excluded and dropped out of use.
Each autopilot swith controls all the axes of the airplane that are autoflight funcitons. This means that if Autopilot A is engaed, it engages each o the pitch, roll, or yaw functions assigned.
Autopilots may have a "manual" and a "command" Command engages more components and more effectively, than Manual. Manual is generally a fail-down mode which is capable of less than the full autopilot can do. In manual mode, the autopilot may only capable of holding altitude and heading. It's a limited feature Generally one moves the associated lever to manual to hold present pitch attitude with a wing-leveler. That's it.
Each autopilot is fully capable of doing the things the others can do, and to do it independently of the others.