The term "Hard Top Convertible" was coined in the early 50's to refer to a new automotive body style. I wish I knew who started the phrase and which car manufacturer produced the first one. The Hard Top body style was originly designed to simulate the appearance of a soft top convertible, a real convertible if you wish. The basic body style was a coupe or two door sedan but the frame and body did not require the reinforcement that a real convertible required to compensate for the lost structural strength from not having a solid roof. Other production costs would still be considerably less than that for a rag-top but more than for a regular coupe.
In addition to removing the post between the side windows and the frame around the door windows, the wind shield was shorter and the roof itself was thicker in profile. Real convertible roofs were thicker because of the mechanisms to raise and lower the top. The rear window and roof support pilars were also modified to give a more convertible like appearance. Most hard tops were two toned with a white or canvas colored top. ( some were also nearly black on top as there were rag tops with black or nearly black soft tops ) . The attempt to simulate the appearance of a soft top, did not end with the outside structural changes and colors. On the inside, there were usually other simulations such as white or canvas colored head liners with chrome immitation bows to support the immitation soft top of course.
There were no dome lights in most hard tops, and some had side courtesy lamps for the rear seat passengers just like a real convertible. There were numerous other small details that helped complete the simulation, for example sun visors were the narrower convertible style and side windows required weather seals attached directly to the glass. Some hardtops had convertible irons placed on the rear roof support pilars.