I'm not quite getting what you're asking, but if you're asking about who's qualified to teach what, it really depends.
Coaching is regulated really spottily. Some rinks are really strict, others are not strict. Some rinks require all group lessons to be taught by coaches with insurance, some allow higher level skaters in high school to work as teachers on lower level classes (like tots) under the supervision of a coach, and other rinks let adults with only basic skating skills teach beginner classes.
Within non group lessons, most coaches can coach most things. In order to coach a skater through certain things, you need to meet certain requirements. All coaches need liability insurance and to be registered with the governing body their skaters compete/test in (USFSA, ISI, Skate Canada, etc.). In the past (not sure if this is still the case), a coach would have to have passed the test (or an equivalent adult track test) in order to be at the boards while their skater is testing that test (ie. if your skater is testing Intermediate moves, you would have to have passed Intermediate moves or Adult Gold moves yourself). For competition, standards are actually more lax. All you have to do is take and pass a certain number of PSA continuing education hours each year to get a certification level. There's a few different levels including one allowing coaching at local/regional competitions, one allowing coaching at national competitions, and another for international championships. Depending on your experience and how well your skaters perform in tests/competitions nationally and internationally, you can also get special merit designations through the PSA to denote your excellence in coaching.
Because of this, I'd say that if you're learning something basic, like just moving across the ice without falling or standing up, it's totally fine to learn it from a skater who's not a coach.
On the other hand, if you're learning something harder and more risky (jumps, spins, turns, field moves, etc.), you should learn it from a coach. Of course, you want to choose your coach carefully based on what you want in a coach and what you want out of skating. Some good things to consider are: How do the other coaches at the rink see the coach's personality/level of expertise/trustworthiness? What system do their skaters compete in? What certifications and experience do they have? Does their area of expertise match up with what you want to learn (Jumps, Spins, Moves, Dance, competitive coaching, choreography, Synchro, recreational/ISI skating)? What do they expect of their skaters (time investment, testing only, competing)? ISI only coaches are great if you want to skate for fun. If you're skating to pass tests or do local competitions, you'll probably be fine with most coaches that coach USFSA. If you want to be competitive at a national/international level, you'll want to get the best coach at your rink or maybe move to another rink.