There is no "standard" difference.
If you are working in an AEA environment, most of the time the difference will be the ASM will be (most likely) on an AEA contract, and have to abide by those rules, while the PA will not.
As far as specific duties, that will always be left up to the specifics of the organization and the team how the divide the work load.
On Broadway shows, often, there are army of PA's up until open, and then they pull back to just AEA contracts, perhaps keeping one PA for a variety of tasks - but again, it will always depend on the specifics of the show. In my years in regioanl theater, I uses PA's as a second ASM, and will assign duties to them based on their personal strength.