The answer to 'types of AC' is there are several main types of air conditioning systems used in homes. The most common are central air conditioners, window units, ductless mini-splits, and packaged terminal air conditioners (PTACs).
Central air conditioners are the most popular type, with an outdoor compressor/condenser unit and indoor air handler that circulates cool air through ductwork. Window units are self-contained, portable ACs that fit in a window opening. Ductless mini-splits have an outdoor compressor and one or more indoor air handling units that don't require ductwork. PTACs are often used in hotels and apartments, with the entire system contained in a single unit that mounts through a wall.