Professionally, SM vs ASM is a contract issue - these are the only two AEA Positions available in stage management.
PSM, SM, First Assistant, Second, Assistant, etc . . . are all billing titles, negotiated. AEA goes back and forth and how to deal with these billing issues.
In America, I feel production stage manager has the following nuances . . . .
1) A PSM oversees other Stage Managers, often oversees someone with the title of stage manager, or multiple ASMs.
2) A PSM tends to be the senior Stage Manager among a group of stage managers.
3) A PSM can be a staff member at a resident theater.
4) A PSM is responsible for hiring / assembling the staff.
5) A PSM is artistically responsible for maintaining the show - technically, acting, putting in understudies . . . which means the PSM may not call every show so that they are able to step out and watch the show and take notes.
6) A PSM is responsible for the training of replacement stage managers.
7) A PSM is the stage manager who reports directly to General Manager / Production Management / Producers.
Often a PSM, especially on larger productions may not be in the rehearsal room at all times.
So, yes, you might have done what will be considered a PSM position in the professional world, but I think to be fair, for a resume, it comes down to billing - how were you billed in the program? What were you referred to as during the production?
I have times been doing an ASM"s job, but was only a PA. There are times when I was billed as SM, but I was more of an PSM.
My advice is to list as SM . . . I can private you and tell you the woes of fast tracking yourself too quickly to PSM level . . .