Multi
Channel, which is the same as AVR and "HT" receiver as well, as Jerry notes. Different terms, all referring to the same thing.
An AVR will support more speakers (most 2-channel receivers don't support .1)
Most stereo receivers on the market now have a preamp out for the sub, but almost none of them have bass management, meaning manual calibration with a SPL meter. The only one I can think of that has a selectable X-over is the Outlaw RR2150. This is another big reason to go AVR over stereo receiver.
An AVR is more likely to have room correction.
Less of a necessity with 2ch.
An AVR is likely to decode more encoding formats.
Irrelevant. For 2ch, you feed 2ch analog or digital and pretty much every device will have that and the ability to downmix to stereo.
An AVR is capable of doing video.
Stereo receivers typically handle audio as well, but I have not seen any that support HDMI or high-def video. Again, if you want video to go through the receiver for switching, you need an AVR. Integrated amps don't have video or any sort of processing (meaning analog only, no bass management, no sub pre-out), while stereo receivers typically have digital audio inputs and the ability to decode. With analog video going away, I am sure we will soon see stereo receivers with HDMI. Likely on the next generation that comes out.
Honestly: I've never been able to come up with a good case for a 2-channel receiver; even in my 2-channel setups.
I am
completely the opposite. For stereo music only, I don't see a point in using a receiver with more channels or electronics than you need. A comparable integrated amp tends to have a better pre- and amp section than an equivalently priced AVR in my experience, and I've always used an integrated for my music systems (no sub).