What are the differences between the different types of TCAS?
The Traffic Collision Avoidance System TCAS (also called ACAS - Automated Collision Avoidance System) is used in aircraft to alert the pilots about possible collision.

The basic system in all the levels are the same. As per the FAA what differs is the type of warning issued to the pilots. As per FAA: 


  TCAS is a family of airborne devices that function independently of the ground-based air traffic control (ATC) system, and provide collision avoidance protection for a broad spectrum of aircraft types.  All TCAS 
  systems provide some degree of collision threat alerting, and a traffic display.  TCAS I and II differ primarily by their alerting capability.


TCAS I issues 'traffic advisories' (TAs) to the pilot, alerting him to the impending collision.

TCAS II provides the pilots with resolution advisories(RAs) in addition to TAs. Basically the TCAS provides the pilot with the required escape manevores in th vertical direction.

TCAS III and IV were supposed to provide horizontal resolution RAs, but development was stopped due to limitations of the available TCAS antennae.

TCAS is expected to be replaced by automatic dependent surveillance – broadcast (ADS–B)