Wetsuits are available in a variety of styles, including shorties (which extend to the knees and elbows, or shoulders) and full piece / one piece suits which cover the whole body. They also come with or without a hood and sometimes enclose the feet.
Wetsuits tend to be made from neoprene and range in thickness from 2mm to 9mm, depending on your requirements. Shore wetsuits are a great example of sports performance wetsuits which are thin, and therefore highly flexible, but for cold water diving you may want to choose a thicker wetsuit. This will restrict your mobility but will keep you warmer.
Semi-dry wetsuits are full suits with inner seals, usually around the wrists and ankles. They are in effect a type of wetsuit; however the seals prevent water from leaving the suit which means it will stay warmer against your skin, providing better thermal protection than a wetsuit. They tend to be cheaper than wetsuits, and easier to use.
Drysuits feature seals at the neck, ankles, and wrists which prevent water from entering the suit, so the wearer stays dry in the water and is insulated by a thin layer of air next to the skin. Many divers also choose to wear a thermal bodysuit under their drysuit, for maximum heat retention; however this is only possible when wearing a fabric drysuit as opposed to a neoprene drysuit, (see: what is neoprene?)
(example of a neoprene knee protector)
This can make parts of the scuba outfit quite bulky and hard to manoeuvre in.