Roadster - 2 Door, 2 seater with no fixed roof (think early Viper)
Spider - 2 Door car with a removable/retractable roof
Convertable/Cabriolet - Any number of doors and a removable/retractable roof
Targa - Any number of doors with a removable roof mid-section
Coupe - 2 Door car with no hatch (also called a berlinetta)
Hatchback - 3 Door car with a hatch
Sedan - 4 Door car with no hatch
Wagon - 4 Door car with a hatch
Ford may call it a sedan, but they are technically incorrect.
Anyhow, a notchback is slang for "coupe" in mustang speak.
"A sedan seats four or more and has a fixed roof that is full-height up to the rear window. Most commonly it is a four-door; two-door is rarer but they do occur (more so historically). In the U.S., this term has been used to denote a car with fixed window frames, as opposed to the hardtop style where the sash, if any, winds down with the glass. As hardtops have become rarer, this distinction is no longer so important.
A two-door sedan is defined by the SAE as any two-door model with rear accommodation greater than or equal to 33 cubic feet (0.934 m³) in volume (a calculation made by multiplying the legroom, shoulder room, and headroom). By this standard, the Chevrolet Monte Carlo, Ferrari 612 Scaglietti, and Mercedes-Benz CL-Class coupes are all two-door sedans. Only a few sources, however (including the magazine Car and Driver), use the two-door sedan label in this manner.
In the popular vernacular, a two-door sedan is defined by appearance and not by volume—vehicles with a so-called formal roofline are called two-door sedans, while those with the more common sloping backlight are called coupes. This has led to the so-called four-door coupe, which is a sedan with classic coupe-like proportions. The designation was first applied by Rover to a variant of its P5 from 1962 until 1973. It has more recently been adopted by DaimlerChrysler for the Mercedes-Benz CLS-Class, which the Mercedes marketing department has erroneously called the first four-door coupe.[citation needed] Other companies are leaping into the segment as well, but the term four-door coupe is entirely aesthetical, and not the product of any formal definition. To make matters even more clouded, the Mazda RX-8 meets the volume requirement to be called a sedan, but it has vestigial rear-hinged rear doors, making it a 2+2-door sedan."
"Notchback is a very common form of automobile body characterized by a sharp vertical drop-off from roof to trunk, as opposed to hatchback or fastback. All notchbacks are what is known as 3-box designs - seen from the side, three seperate volumes - the engine area, the passenger area, and the trunk area.
The notchback is usually a synonym for sedan, although many coupé cars are notchbacks as well. Notchback can also refer to liftback or hatchback vehicles, if there is a discontinuous line from roof to rear fender."