Fastback describes a profile: the roof drops in a single line from its highest point to the tail, with no notch above the rear window and no vertical panel closing off the back. It says nothing about the boot. A fastback can have a sedan’s separate lid or a liftback’s full tailgate, and telling which is which means looking at the shut lines rather than the silhouette.
The shape arrived in the 1930s as an aerodynamic idea, spent the 1960s as an American styling signature, and has returned for the original reason. Cutting drag is the cheapest range a battery car can be given, and the taper does it without touching the powertrain. The MG 07 and the smart #6 both use it. The costs land in the same two places every time: rear headroom, and how much of the boot opening stays usable once the glass slopes into it.