The first kind is usually an older coach of elite skaters in the national or international competitive ranks. Their students get their instructions at the board, then use as much ice as they need to build up speed, demonstrate flow and perform their element. These skaters are getting tweaks to already high level techniques. Their skill in avoiding other skaters is superb and when they skate back to their coach, they are aware of traffic.
When I see a coach-skater pair like this on ice, I am filled with humility. I will never skate that good, that coach will never look at me as any thing other than slow traffic, but the fact that I know where the coach is, I can easily avoid the much, much, much better and much much much faster skater. My job is to stay out of their way. ... so far, so good.
The second kind of coach who coaches from the boards:
This coach leans against the boards, frequently positions herself at the end of harness alley, and her little student skate no more that 6 feet away to do their hoppy little jumps. Her little students don't look for traffic, and since they're barely away from the boards, they block anyone going along the boards to stay away from a skater in a MITF, dance or program.
Sometimes there's three of these coaches lined up against the hockey boxes, their little students forming a beehive of activity concentrated along harness alley.
Some of these coaches are so lazy, they draw their 3 turn and mohawk patterns with their Marker of Doom no more than a couple of feet away from the boards; their little students will camp out there all through freestyle and sometimes public after, blocking traffic long after the coach is gone.
I think I've heard all the rationales coaches have for this; their feet hurt, they're pregnant/recovering from a pregnancy/had a kid ten years ago and OMG she's still tired, they don't want to move their student out in the middle because it might interfere with patterns, there's too many skaters on the ice and adding another coach would make it worse.
Yes, I hates this. I've noticed most of their students have hoppy little jumps, limited flow, and don't build up speed because they're never more than 10 feet from their coach and they're learning jumps in a high traffic area. It's gotta take a long time to learn technique that way.
And you, you coach from the boards coach, you scare the daylights out of everyone when you have one of your little skaters do a lutz in the lutz corner during public.