As a general rule - In a highschool, you are asked to SM _ONE_ show, or rather, to be the SM of _ONE_ show. Hence, you usually become the DSM or PSM or just the plain old SM. 6 of one, half a dozen of the other.
Actually, I lied a bit before. Truthfully, in australia we tend to use 2 different naming conventions for within a show - those for a musical/opera/operetta, and OTHER. Here is a brief equivilancy list assuming that the person who calls the show also rehearses it.
Musical : Other
DSM : SM/PSM
SM/ASM : ASM
Outside of the single show, you have your company SM. They have a contract with a certain company (as opposed to being contracted to a show), which says that for a certain period of time (arbitrarily, 12 months) you are a stage manager for the company. Usually, the CSM is 'above' the PSM/DSM in the heirachy of things and they usually keep the entire show (and company) running smoothly.
I mentioned above that the equivilency assumed that the same person called as rehearsing, if there are separate people:
Musical : Other : Job
PSM : PSM : Production up to tech week
DSM : SM/Calling SM : Tech week and beyond
SM/ASM : ASM
Basically though, don't worry too much about titles unless you are in a professional theatre - amdram/student theatres often do not have the people, budget and skillset required to have all the levels of stage management, and the jobs are usually not as defined.