Hardtop vs Coupe vs Sedan

Notchback is what we call it, it is still a hardtop...

Notchback is what Ford called their non-fastback Mustang. Or at least Mustang fans started calling them that. No Barracuda should ever be called a notchback.

Plymouth called its non-fastback hardtop a "hardtop coupe." And the Road Runner a "2-door coupe." This is direct from the 1968 factory dealer brochures.

And would you believe the 68 Barracuda convertible was referred to as a "convertible coupe"?

Fact is, the word "coupe" does not have an established definition, and over the years has been applied in a variety of ways to a variety of body styles. But probably most often to 2-door sedans.