These terms thoroughly confused me when I first started looking into CIS. To make matters worse, they can go by different names and people also tend to get them mixed up (such as by saying AAR when they mean AAV) and the AAV and the Decel Valve kinda even look the same. Heck, I've mixed them up just reading the letters.
I'll try my best to help un-confuse things.
For more info, see boyt911sc answer in post #3 here:
http://forums.pelicanparts.com/porsche-911-technical-forum/738758-whats-difference-between-aar-aav.html
AAR on the left and AAV on the right. (picture courtesy of boyt911sc)
Auxiliary Air Valve (AAV)
The AAV provides extra air on startup. When the vacuum reaches a certain point, the AAV closes off.
Test procedure:
http://forums.pelicanparts.com/porsche-911-technical-forum/740422-how-test-auxiliary-air-valve.html
Auxiliary Air Regulator (AAR)
The AAR provides extra air when starting a cold engine. Like the WUR, it has an internal bimetallic strip that is heated via an electrical connection. When the engine is first started, the valve is open. This also causes the higher initial idle at startup. The AAR gets power from the same fuel pump relay circuit as the the WUR. As the strip heats it slowly closes off the valve, reducing the airflow into the throttle and reducing the idle speed.
Test procedure:
http://forums.pelicanparts.com/porsche-911-technical-forum/112138-aar-good-bad.html
Adjustment:
http://forums.pelicanparts.com/porsche-911-technical-forum/200906-aar-revisited.html and
http://forums.pelicanparts.com/porsche-911-technical-forum/551321-auxiliary-air-regulatory-adjustment.html
Deceleration Valve
The decel valve (called the "vacuum limiter" in the PET and also sometimes referred to as the "auxiliary air device") is the third component that can bypass air around the throttle. The purpose of the decel valve is to prevent an overly-rich condition when the throttle suddenly closes. The result is a slower throttle response. Some people do not like the slower throttle response so it is not uncommon to find the vac line connection disconnected and plugged, as well as the connection on the decel valve itself. The decel valve looks deceptively similar to the AAV. If the diaphragm in the decel valve leaks, it can cause a high idle.