Both ISI, the recreational federation, and USFS, the competitive federation, have figure skating tests, broken down into progressively more challenging sets of skills. These test levels also generally correspond (but only generally) to competition programs.
However, the scoring on tests is very different than the scoring on competitions. For one thing, while there is a scale, the tests are essentially Pass-Retry. (The kinder, gentler, 21st century way of saying Pass-Fail. Musn't upset the kiddies or their check-writing parents, I guess.) There is a minimum passing score, for skating that meets the test standard. If you exceed the test standard, you can get a higher score; in USFS testing this is the rarer case. Most skaters pass AT the passing score because the passing standard is high and fairly universally agreed upon by nationally trained test judges.
I have heard at least two parents complain to their children that they "barely" passed a USFS test, i.e. got just the passing score. This is wrong. In USFS testing a pass is a pass. The standards are high; everyone passes with an A. Passing over the minimum score is equivalent to an A+. One parent told me she was going to make her daughter retake her test because "I wasn't happy with her score." First, this is not allowed, and second, sorry, that's the stupidest thing I've ever heard from a parent, and I've heard a lot of stupid things from parents (and said a lot of stupid things AS a parent).
Unlike USFS, which uses a descending point system (10 point scale, your score is the accumulation of your deductions), ISI uses more of a grade system, 0 through 10. The handbook describes it as follows:
0- didn't attempt
1- attempted, not recognizable
2- attempted, recognizable
4- not passable (F)
5- minimum passing grade (D)
6- Fair (C)
7- Good (B)
8- Very good (A)
9- Excellent (A+)
10- Superior, no errors (A++)
So as you can see, in ISI, you pass with a "D" just like in school.
I really don't like to see this however; who wants their kid to pass with a D? I don't think I'm alone in this either. Because ISI makes me pass Ds, I give more 3s and 4s than I might otherwise. I also really disagree that a "5" is a "D." Coaches that I know are looking for better than a D. You can't do only 70% of an axel, after all, which would be a D. I tell my students that you should not move up a level until you have at least one, and better yet two 7s in your scores. Further, I think that a teacher who gives all 5s is not paying attention. There are six skills in each test; I find it difficult to believe that all the skills are going to be equally just 5s. I have also observed that passing with all 5s is a guarantee that you will struggle at the next level. My grading looks more like this:
0- did not attempt
1- attempted, no understanding of skill
2- attemped, cursory understanding of skill
3- completed skill, unacceptable errors
4- completed skill, minimal errors
5- good understanding of skill, passing
6- skill is good enough for competition
To compete in ISI competitions through Delta you must complete an isolated skills test; to compete in Free Style you must also take a program test (all skills set to music). In USFS you need to do the Moves and Freeskating tests at each level to compete at that level. You can also "skate up" a level at some USFS competitions. You cannot skate up in ISI. You cannot skate down in either system. (Deliberately skating down by not taking a test you are ready for is called "sandbagging" and is considered cheating.) In both systems, your class level has no bearing on your test level. You can take classes both above and below your test level, depending on what your program or your coach requires or tolerates.
USFS tests must be taken in front of judging panels of varying sizes and judge's levels. They do not need to happen only at Club test sessions. Your coach can arrange separate, non-club tests if needed; you just have to pay for the ice. Club test sessions are a convenience, not a requirement. Talk to your coach and club leadership to find out about this. I took my First Figures test on a public session with a single Silver level judge (it was an utter disaster because you really can't skate figures on public, but the point is, you can do this).
ISI tests through FS 6 can be taken at your home rink. It is generally frowned upon to test your own private lesson student, even in class, but is not specfically against the rules. Each rink should have its own rules about testing-- some allow students to move up just from class tests, some set up special ISI test sesssions, some allow class testing to move up in the classes, but require a separate test to qualify for ice show solos. I've worked at 5 different rinks, and seen 5 different test arrangements. Above FS6 you must take the test at special sessions with impartial judges. Coaches are judges in the ISI system, with judging levels of Bronze, Silver, Gold.