A retractable hardtop — also known as "coupé convertible" or "coupé cabriolet" — is a car with an automatically operated, self-storing hardtop, as opposed to the folding textile-based roof used by traditional convertible cars.
A Volvo C70 with retractable hardtop
1934 Peugeot 401D Coupé transformable Eclipse (Pourtout)
1934 Peugeot 601 C Eclipse
1934 Lancia Belna Eclipse
A hardtop is a rigid form of automobile roof, typically metal, and integral to the vehicle's design, strength, and style.
1965 Rambler Marlin, a pillarless hardtop
1969 Australian Dodge Phoenix four-door sedan has a B-pillar and painted window frames
1969 Dodge DE Phoenix 400 pillarless hardtop coupe. The lack of a B-pillar and window frames, added vinyl roof, thickened C-pillar, and softened roofline creates an appearance similar to a convertible.
1976 Chrysler New Yorker with doors open. Note the absence of a driver's vent window and half-height pillar to which the rear doors attach.