Although there are many words used for different types of convertible cars, in my opinion, the difference between the numerous names of body types makes sense only for those interested in classic models. Below I’m explaining why. As to modern makes and models, for the most part it’s nothing but choosing between hardtop and soft top models.
While with the classification of different types of convertible cars based on roof rigidity and the material it’s more or less clear, the body and roof construction classification is more vague. For a example, the same term may be used for cars with different body styles and roof types, like “coupe” for both fixed-roof and convertible cars, or different terms may be used for the same vehicle body type. Such a dissonance occurs mostly because the original models specific body type names were first applied to have modified over time, retaining only a few original constructive features and the name of the body style. As a result, structural differences and peculiarities of a specific body type can be observed only in the original antique models that appeared in late 1800s - early 1900s or classic ones. Roadster, coupe, cabriolet, targa tops are actually the types of old convertibles in their original construction, all of which gradually evolved into more or less similar constructions, most often referred to as sports cars, open cars or convertible cars, all of which are either hard tops or soft tops.
Hardtops with rigid retractable folding roofs made out of plastic and metal are opposed to soft-tops with the roofs made of a soft material like durable canvas, vinyl or vinyl coated cloth. Vinyl or vinyl coated canvas is typical for US of Japan manufactured convertibles and canvas tops for those made in Europe. Which type of a soft top is better is just a matter of taste. In my opinion, vinyl and vinyl coated fabric is easier to care and more stain resistant. Hardtops have a retractable roof made of plastic, still and aluminum that folds into trunk space or the space between the trunk and the seat. Other names used for hardtops are: retractable hardtop, drop-head coupes, drop-top coupes, convertible coupes, coupe roadsters, coupe cabriolet. Hardtops roofs are powered, non-detachable, types, except for two models: a certain model of Mazda MX-5 and Jeep Wrangler. Most of both types have 2-doors, but for a few 4-door convertible models, either 2- or 4-seaters. Needless to say, softtops are way cheaper.
Today, the term sports car (in connection with roadgoing cars as opposed to racing ones) is often used as a synonym to a convertible car, with regards to both hardtops and soft tops. However, a sportcar is not necessary a convertible, is can be just any light-weight sporty looking 2-door 2-seater with high maneuverability. Apart from how the manufacturer positions a new sporty vehicle and what exact wording is used, I’d say what is understood under a sports car largely depends upon one’s local weather conditions. In southern regions a retractable roof is something one just cannot fancy a sporty car without, while in the north, where the need for being protected from cold and nasty weather is far beyond the awesome views but the need for speed and maneuverability remains, sport cars may have solid roofs. For example, Mazda MX-5 (Miata), the world’s best-selling sports car, is available in both fixed-roof and convertible (again, both soft-top and a hardtop) variations.
The term coupe car comes from French past particle for the word couper (“to cut”) which was used for two-door cars with a fixed rigid roof, being a classic example of a light-weight 2-door sport car with a solid roof, small, interior and no B-pillar. Today the term coupe car is also sometimes used for hardtop convertibles, although technically it’s not quire correct because a convertible is not a coupe car, where the major criteria have always been the solid roof and 2 doors. That’s why to avoid confusion, convertibles are often called drop-head coupes, drop-top coupes, convertible coupes, coupe roadsters, coupe cabriolet, and actual coupe cars are called “fixed-roof coupe”.
Targa top comes as a variation of a convertible type where not the entire roof can be removed but only it’s cental part, while the rest of the roof remains, the reason why this design is also frequently referred to as a variation of a coupe car or a semi-convertible. The term if fact is a registered trademark of Porsche AG who was the first to use this body type in 1966 Porsche 911 Targa model.
Historically, a roadster (aka spider, spyder), is a 2-door 2-seater with sporty handling, without side windows, with a soft retractable top and the seats retracted to the rear part of the body. Over time, the body type modified into what is now known as a typical sport car. Until recent years the name roadster was used for soft tops, but now hardtops are more and more often included in the category. Actually, a roadster is a synonym to a convertible sports car. The best known representatives of the class are Mazda MX-5 Miata and the Mercedes-Benz SLK300.
Today, rag top is often used for different types of soft-tops. However, in original classic models, like 1958 VW Bug, only the central soft part of the roof was an actual retractable rag, making a window in the roof but nothing above that. The roof was fixed and remained in it’s place, as well as side and back windows, so in order to enjoy the wind and views one would have to stand upright through the roof window and remain pretty much that way throughout the journey.
Cabriolet is actually a French word for a convertible, an open car. The combination “coupe cabriolet” is often used to distinguish between the actual coupe (2-doors, fixed roof) and an open car, as “coupe” started to lose its original meaning.
Droptop is currently used for any car with a retractable roof.