There are two established curricula for figure skating schools across the US: the Ice Skating Institute's Learn to Skate or weSkate program, and US Figureskating's Basic Skills. Both these programs take skaters from first-time on the ice up through triple jumps (in USFS kids transition to high freestyle through their Bridge program), as well as specialties like Pairs, Dance, Figures, etc. Basic Skills also has speed skating and hockey curricula. In Canada the skating federation (Skate Canada) promotes the CanSkate curriculum (see what they did there? Cute.).
There are also rinks that use their own curriculum, but if you then compete in any ISI or USFS competition you have to adhere to the curriculum as laid out in the two federations (ISI has greater restrictions on elements that can be in programs than USFS believe it or not).
ISI is strictly recreational. Although it does have local, national and even international competitions, and trains to the highest level (most difficult test in figureskating is not USFS Senior, but ISI FreeStyle 10) the focus is on fun. Even if you start in an ISI program, if you want to compete in qualifying competitions leading to Nationals, you must eventually switch to the USFS Moves and Free Style tests. It is possible and common for skaters to do both.
So that's the outline. What's the difference?
Both curricula are designed to lead the skater in a logical progression through the skills; to "build" each skill as it were. From two foot to one foot glide, to glide on a circle (edge), to crossovers. Then do it all over again backwards. Then combine forwards and backwards (turns). Add jumps, spins, more complex turns, etc.
ISI is a goal oriented curriculum. The skills are basically stated as "Forward Crossovers," "Backward Crossovers" "Three-turns" et cetera, leaving the instructor to break the skill down into the necessary glides, rotations, body alignment etc. A successful coach in ISI needs to understand the details of each move, because the curriculum doesn't hand it to you.
Basic Skills is very process oriented, and relies less on the knowledge and creativity of the teacher, but it forces students to really master each individual component of each skill.
I like the way Basic Skills forces a teacher to break the skill down. The drawback with the curriculum is that it breaks the skill down so far, with 7 testable skills at every level, that it removes a lot of discretion and creativity on the part of the coach, and just takes up a lot more class time on each line item skill. This is part of an educational approach called "deskilling" as in the teacher doesn't need actual skills to teach. It is directed at the idea of anyone being able to teach anything if they just follow the curriculum exactly, whether they're a trained teacher or not.
I like the way ISI makes it very clear to the student (and the parent) exactly what it is they are learning. "Forward Crossovers" is way clearer than "forward alternating half pumps on a line, then pumps on a circle, then forward inside and outside edges on a circle, then crossovers" (which spans 3 separate levels, but are all aimed at teaching crossovers). ISI forces skaters to connect the dots. My experience of Basic Skills was that kids just do not really get the connection between stroking, pumps, one-foot glides and crossovers, because the curriculum decouples the skill from the goal.
The drawback with ISI is that kids get "stuck" and it's harder to demonstrate why to the frustrated parent. In Basic Skills you can see that you have to have a solid one-foot glide on a circle before the crossovers. In ISI it's just "can't do crossovers."
Kids learn to skate no matter which curriculum they use, or neither. The key to learning how to skate is mileage. If you keep taking classes and lessons, you will get better, ipso facto. You will get best if you allow the teacher, and not the parent or the kid, decide when a child can move on. Slower is better. As I said to a child today, bored with edges, "in 5 minutes, you will get to do whatever you want. Is agonizing boredom for 5 minutes something you can handle?"
I like the way ISI leaves the breakdown up to the coach. Unfortunately this does not work if the coach does not know how to break down the skill.
So what's the solution? ISI requires coaches with a clue. USFS has the better skills progression. Coming up with better skills progressions and lesson plans is a favorite coaching parlor game.