Intra-interface--anytime an ASA receives traffic on an interface and it is to route the traffic back out the same interface
Inter-interface--anytime an ASA receives traffic on an interface and is to route the traffic out another interface of equal security level.
So I think this is exactly what you are saying. The command is to permit traffic that is sourced and destined to the same security level. When we are bouncing traffic off a single interface, that interface can have only a single value. To me it's just easier to think about it in terms of "intra" meaning "within" or "same" as opposed to the use cases of the command. So anytime an ASA receives a packet on the outside interface (could be any interface) and that packet must go out that same interface, that would be intra interface. It could be encrypted, or not. Inter means between. So anytime traffic is going between two interfaces of the same value, this is required if there are no acl's to permit the traffic. HTH
Inter is between two different interfaces with same security level. It can also be two sub-interfaces of same physical interface.
As you said, "Intra" is used during hairpining. The best example is when EzVPN client connects to ASA (Server) with no split tunneling. The internet traffic from the client is routed by the ASA. Any internet from client comes to ASA and is routed back through the outside interface to internet.