Usually, the CSM is 'above' the PSM/DSM in the heirachy of things and they usually keep the entire show (and company) running smoothly.
Here is where its different between Australian & British theatre and American theatre. Here in the states we don't use the titles "Company Stage Manager" and "Deputy Stage Manager". Here's a brief list of what the roles tend to be:
ASM: US: assists SM
ASM: AU/UK: assists SM, can also be prop person
SM: US stage manager
DSM: AU/UK for "Deputy" - roughly the equivalent of a US stage manager - is the one who actually calls the shows
PSM : US - usually someone in charge of an entire season of shows, not just one show in specific.
CSM: AU/UK - the equivalent of a US PSM, thought often has aspects of a US Company Manager and Production Manager
Yeah - I know - I used Company Manager and Production Manager without the "S" in the middle - those are other jobs in management.
That's about as basic as I can break it down - and even then that's really over-simplified. As a HS student, you're basically a SM. The other roles are for larger companies - just think of it in terms of the more people there are to deal with, the more people you need to deal with them.
But these are also just basic guidelines as well - often companies will create titles to suite their purposes/ interpretations. Its just something to be aware of - but be sure to ask a company what the job role is as they see it when you apply for something.
-Centaura