Hardtops were cars without the B-pillar extending up to the roofline, but rather, made just long enough to support the door hinge/jamb so that when the front and rear windows were open, there was an unobstructed opening from the windshield post to the rear window support. The B-pillar was short (half-height?), attached to the frame, was very rigid, and aptly supported the rear door hinges.
Four doors are no longer hardtops (but really sedans) since modern cars utilize unibody construction (not frames, per se), which integrate the B-pillar as part of the roof support in case of a rollover. The modern incarnation of the Charger is one example. When you open all of the windows, the opening between the front and rear windows is interrupted by the B-pillar, which supports the roof and the hinge for the rear door. Most manufacturers paint or black chrome the B-pillar window frame to make the four door sedans LOOK like the old hardtops. But when the windows are down, there's NO mistaking a sedan for a hardtop.
The difference is easy to see when you compare them side by side.
Here's a 2006 Dodge Charger four door sedan. Here's a 1967 Pontiac LeMans four door hardtop.
See the difference?

BTW......the 2008 Challenger prototype is a two door hardtop (although Dodge states that it's a coupe, having only 2 doors) - there's no B-pillar rising to the roofline between the door window and the rear side window. When the front and back side windows are down, it's a continuous opening from the windshield posts to the rear windshield roof supports.
............the Ford Mustang is a two door coupe (2 doors). What makes it a coupe is that the rear window doesn't go down, and the back seats are more an after thought than intended for use for comfortable seating for two adults. It's more like the old 2+2 configuration. If the B-pillar wasn't fixed (to the roofline) immediately behind the front door, and the rear window operated, it would be a two door hardtop.
Again, you can compare; The 2008 Challenger two door hardtop (scroll down to boredout's post - thankyou!), and the 2006 Mustang GT 2 door coupe.

Keep in mind, the "hardtop", "coupe" "sedan" and "2+2" references I use are by the old standard, based on window/B-pillar configuration. Modern references are that 2 doors are all coupes and 4 doors are all sedans - simply because of the number of doors.