'Not...anymore' refers to something that occurred for a short duration, or an instance, whereas 'not...(any) longer' refers to an extended period of time.
E.G. "He isn't there anymore" - This means he was there, but only for a somewhat brief period of time.
"He isn't there any longer" - Implies that he had been there for a while, and he has now vacated that position/area/etc.
Hope that's what you were looking for.