I'd like to add that a jog and a lope aren't exclusively Western things. Thunder has both a jog and a trot, and a lope and a canter. With his jog, as in every jog, there is minimal knee and hock engagement and the overall motion is flat and smooth. He has a horrendous draft horse trot, very up and down with higher knee and hock action and it will darn near knock the fillings out of your teeth. The difference between his lope and his canter is less marked but it's still there - again, minimal knee and hock action and much smoother ride overall.
I've yet to find Dreams' canter, though he also has a definitive trot and jog. When pressed Dreams' lope will get faster, his strides longer, but it never really changes in smoothness nor in engagement of his hocks and knees. It's just as easy to sit loping slow circles in the arena as it is moving right out on the trail. Just faster motion, is all.