The answer to 'types of central air' is that there are several common types of central air conditioning systems for homes. The most popular are split systems, packaged systems, and ductless mini-splits.
Split systems have an outdoor compressor/condenser unit and an indoor air handler or furnace. This is the most common type of central air system. Packaged systems have all the components - compressor, condenser, and air handler - in one single outdoor unit. Ductless mini-splits have an outdoor compressor connected to one or more indoor air handling units, without the need for ductwork.