Sorry for the delay.
It’s true, international isn’t all that specific. However it at least implies a certain minimum of services and ability to handle large aircraft types.
I also like the aerodrome proposal and see it used often in large airports. However that is not my focus right now.
As for the “local” confusion, of course a local airport can have a regional connection, otherwise smaller and larger airports wouldn’t be able to be connected.
It also isn’t an axium that someone can’t travel long distance from a local aerodrome, all it implies is the level of service, infrastructure, aircraft type and route type that happens at an aerodrome.
A regional aerodrome will have a substantial amount of regional flights while a local aerodrome will be majority local.
A regional aerodrome will have control services, de-icing, terminal, catering, security, passengers services etc. approaching that of a national hub while a local airport would have more basic services like only tower information, maybe fuel, no catering, hangars, a protected runway etc.
A regional airport can handle a large flow of larger, medium sized passenger aircraft and small general aviation aircraft while a local aerodrome might only be able to handle a couple medium sized planes and the local small private aircraft.
It implies a lot about a lot about the amount of traffic, the category of that traffic and the services necessary to support that traffic flow. A regional aerodrome that support traffic covering a whole region while a local aerodrome can only handle the traffic from a few towns.
Since there is a big difference between these, separating “local” from “regional” would be very useful.