Ahh, the faithful AQHA handbook of rules and regulations.
I think everyone should have to read it before they mount a horse... but that's just me.
I could give you my own version of the definitions as I've read them, but I'll just copy some verbatim selections.
447. (a) (3) The lope is an easy rhythmical three beat gait. The horse should lope with a natural stride and appear relaxed and smooth. It should be ridden at a speed that is a natural way of going.
447. (b) (3) Canter is a three beat gait; smooth, free-moving, relaxed and straight on both leads. The stride should be long, low, and ground-covering.
I think the canter definition is very straightforward. But some of the western descriptions are open to translation, especially the "natural way of going" part. As a result, it goes on to describe various qualities of the western pleasure gaits in order to further clarify what is poor, average, good, excellent, etc. This is to help them clean up all that peanut roller mess. But I will spare you all that.