At least, let’s not forget that not all aerodromes are airports, and even that not all air strips are aerodromes. Applying an airport classification to aerodromes is like deciding if a mammal is a dalmatian, a bulldog, a terrier or a spaniel.

Aerodromes are usually classified according to abstruse aeronautical criteria, while airports are classified according to more commercial criteria. In France for instance, as far as I remember we tend to distinguish between passenger airports, cargo airports and industrial airports.