ʿAmm concerns multiple members included under one meaning. Mushtarak concerns different meanings conventionally associated with one word.
ʿAmm: “all students” — one concept, many members.
Mushtarak: al-mushtari — buyer or planet, two distinct concepts.
The first question is which members fall within a rule. The second is which meaning is intended in the first place. Specification and choosing between meanings are separate interpretive operations.