A "pro," or "professional," is someone who earns a living from skating, whether coaching or performing. Many clubs and rinks will have a "head pro(fessional)" position, which is the same as saying "head coach."
An instructor teaches skating skills in group or private lessons. Some people call their private instructor a coach, but it's not necessarily the correct term unless they've providing more than skating instruction. If you take private lessons and the professional simply reviews/teaches skills, you have a private instructor, not a coach.
A coach addresses so much more: training, rest, nutrition, equipment, music, choreography, testing, competitions, planning, goals, etc. A coach goes to the test session or competition with the skater to help them prepare mentally and physically whenever possible. Many coaches charge for those services piecemeal, others include it in their hourly on-ice lesson rate.
Most people don't care about using the correct term, as someone upthread mentioned. The point was driven home to me by a very public rant. A skating mom was furious at her son's instructor/coach because he wasn't going to put her son on the ice for his freeskate event at a competition. She said, quite loudly, "Are you his COACH or his INSTRUCTOR? He needs a COACH to compete and I can find someone else to fill that role if you just want to teach." That's the first time I really understood the difference between instructor and coach.
If you don't know what to call someone, ASK. Some use the dance school honorific of "Miss (firstname)" or "Mr (firstname)", others use "Coach ()" and still others say "Just call me Jane." (Olympic Coach John Nicks is referred to as "Mr. Nicks" by almost everyone!)
Titles vary based on the rink, the skating director and the area. At one rink where I taught, the instructors were all referred to as "Coach ()." A new Director was brought in and we were called "Miss (female firstname)" and "Coach (male firstname)." Except for the one woman who introduced herself as "Ms (female firstname.)" Whatever floats your boat - I prefer coach, but I don't object to anything short of first-name only. That's a cultural thing; little kids never called adults by their first names where I grew up. You at least added a Salutation like Mrs or Aunt.
I used to have a student whose father always called me "Coach." As in "Coach, how's my little girl doing?" "Should we be doing more off-ice, Coach?" He must have played basketball or football because he was always so formal and it always made me smile because it was so unusual in that area. (Yes, he knew my name because the DD called me "Miss ().")