The answer to 'types of air handler' is that there are several common types of air handlers used in residential HVAC systems. The most common are central air handlers, packaged air handlers, and mini-split air handlers.
Central air handlers are the most common type, featuring a blower that circulates air through ductwork to different rooms in the home. Packaged air handlers contain all the components (compressor, coils, blower) in a single outdoor unit. Mini-split air handlers are ductless systems with an indoor air handler unit connected to an outdoor compressor.