I didn't know exactly what to call this. Can someone explain to me the different ways a horse walks or runs? Or point me to a website that does? I have no idea what the difference between, say, a canter and a lope is. I need to learn, so I can use the correct terminology.

I found this information (see link below) of the description of the various horse movements, or gaits. It's pretty detailed and informative and I hope it serves your purposes.

http://en.wikipedia.org/wiki/Horse_gait