You could say redundancy, on the basis that if one fails another can be used. When we speak of redundancy in an aircraft, however, it usually implies multiple systems that are in use simultaneously, which allow a fail-down capability.
In normal use, where one autopilot system is used, the other autopilot systems are off. You could think of them as "spares." Each of the autopilot systems is generally attached to a different guidance system, and in many cases, different hydraulic systems. In the airplane I fly, we have four different hydraulic systems three autopilots, and three different IRS gyro systems that work for each individual autopilot system.
The autopilots, in turn, receive inputs from a number of different sources, including air data computers, INS or IRS gyro systems, FMS/FMC management computers, etc. Sub systems such as autothrottles receive input from engine instrumentation or engine sensors, as well as autopilot panels (pilot inputs), performance management computers, etc. For the most part, these systems that feed the autopilots, and the autopilots that control aircraft systems, are independent. Some share components; the autothrottle, for example.
During certain phases of flight, landing on an ILS approach, autopilots may be used in concert with each other. In the airplane I fly, an additional option is available when selecting the navigation mode for the approach, which permits more than one autopilot to be used. In this mode, the electrical solenoids that normally lock out other autopilots and prevent multiple autopilots from being used at the same time, are removed. A computer closely monitors the inputs of each autopilot, and if one gives an indication of doing something that's not in harmony with the approach data or which appears to be in error, the offending autopilot is "cammed out," or dropped out of the loop.
During an instrument approach, certain criteria need to be fulfilled at certain altitudes and certain places during the approach; if these needs aren't met, the autopilot system won't allow the approach to proceed with multiple autopilots engaged. If this is the case, the approach may need to be abandoned, or may need to be continued to higher landing minimums. When flying to low minimums, referred to as "category III" minimums, multiple autopilots may be used to satisfy requirements of the approach. The approach allows the airplane to be flown much lower than a standard instrument approach, including autoland approaches in which the airplane flies all the way to a touchdown.
The use of multiple autopilots could be viewed as extra oversight. Just as using two pilots to fly the ILS and monitor the progress of the approach offers a higher level of awareness and safety, so does the use of more than one autopilot, especially during low minimum approaches. You could also look at their use as redundancy, like wearing two sets of latex gloves during an emergency medical call. One breaks, you've got a second already lined up and flying the approach, "in the loop," ready to go.
In the airplane I fly, I can only engage one autopilot at a time in normal operations. When first engaged, I announce "Autopilot A to Command" (or Autopilot B, etc, depending on which one is selected). I fly an older airplane, which requires me to select the vertical speed mode and navigation modes, and select the altitude mode I need, as well as the autothrottle mode (if used), all independently. By doing this, I have selected the autopilot I intend to use, and then selected all the functions that I intend to input into the autopilot, to tell it what I want it to do.
Once I select an autopilot, the other autopilot(s) are locked out. I can select a mode for the instrument approach which removes that lockout, and which allows more than one autopilot to be engaged; that mode is only available for an instrument approach, and only available for certain approaches in certain conditions.
There's no particular reason why one might choose this autopilot or that. As convention, generally the pilot in the left seat engages autopilot A, and the pilot in the right seat uses autopilot B, but there's no reason why either one couldn't use the opposite autopilot. In our airplanes, the autopilot and flight director (a device on the attitude display indicator, or attitude indicator, which gives guidance on flying the airplane) are tied to a particular side of the cockpit. That is to say, autopilot B will match what's seen on the first officer's display. There shouldn't be any difference between the captain and first officer displays, but they are independent systems, and if the first officer engages autopilot A but views his own instrumentation and flight director, it won't necessarily be showing him what's going on because he's using a different computer and autopilot than he's using for his own flight director.
The difference is generally very minimal. In some airplanes using much older technology such as straight INS units, it's possible to have different information displayed on one side of the cockpit than the other. This is due to drift in the INS units, and other factors. One pilot may be seeing a course needle deflected to one side, suggesting he needs to turn that direction, and a flight director telling him to turn in that direction, even though the autopilot soldiers on, straight ahead. The autopilot is working off data on the other side of the cockpit, and the other pilot shows on his instrumentation what's reflected in the actions of the autopilot. For these reasons and traditional convention, generally each pilot will use his or her "own" autopilot, though it's not at all necessary.
Sometimes a problem may develop with an autopilot or autopilot channel. A document in the airplane known as a "minimum equipment list" allows us to fly with inoperative items or equipment, so long as certain requirements are met. An autopilot may be "MEL'd" out of service, in which case the operative autopilot(s) will be used. The choice of which one to use may be dictated what's functioning at the time.
It's also important to remember while discussing autopilot and their use that the autopilot doesn't fly the airplane. It's a control system, just as using the control column is a control system. In neither case is the pilot actually moving the control surfaces of the airplane, but making an input to the airplane. When manually moving the control wheel, for example, I move a cable, which moves a hydraulic valve, which sends hydraulic fluid to an actuator at a control surface, which moves the surface. When making an autopilot input, I tell the autopilot where I want the airplane to go, or what I want it to do. I may roll a small wheel on the center pedestle or on the forward instrument panel, for example, rather than moving the control column; the autopilot is just another method of controlling the airplane.
Autopilots often don't have rudder inputs because the rudders are often used very little, particularly in phases of flight in which the autopilot is in play.