Often just called convertibles, these vehicles have a roof that either moves out of the way or comes off. This is mostly done for driving pleasure, but it often drastically changes (in comparison to the standard version) the car's driving characteristics.
The major visual difference is usually the shape of the roof, since it has to either fit in the trunk, or is made from a fabric which stretches over a metal frame.
Convertibles Are Usually Heavier
One would think that replacing a metal roof with a cloth one would reduce weight because cloth is lighter than metal. However, due to the lack of a supporting structure in the top half of the middle of the vehicle, designers have to compensate with a rigid floor, and the amount of metal required to make that support is heavier than the metal roof would have been.