I wouldn’t call myself a team roper nor an expert on the subject but I team rope on occasion for fun and I used to ride for a 10x NFR qualifier years ago.
I’m not real sure what you want to know? It is different than branding calves or doctoring cattle outside, not all roping is created equal.
Difference between head and heel horses is just that. For me I prefer a head horse who is quick to catch cattle, rates and is strong enough to take a jerk and tow a steer so he may bigger and have a bigger stride.
Heeling, I prefer a horse a bit smaller and has a shorter stride to match a steer hopping makes it easy to get in time with and a big stop. For me, creating that stop and distance makes for the best heel shot and gets things shut down faster.
A long time ago team roping horses weren’t very broke, they had one job. Now they are realizing the horsemanship, the horses are getting more broke and a lot of cow horse and cutter rejects go to the roping pen.