TCAD is the acronym for Traffic Collision Avoidance Device and is the low end of traffic systems, usually consisting of a passive transponder receiver. TAS is the next step up and consists of an interrogator that transmits to transponders on 1030 MHz, which reply on 1090 MHz and using the time to reply to calculate the distance to the target. TCAS is the top of the line and in addition to TAS, provides the pilot with an RA (Resolution Advisory) to climb or descend to avoid a collision. The Garmin and other systems support a common interface to display the traffic information. There are limits on this interface, particularly in how the information is encoded on a map page as this requires a heading input. Without a heading input, the Garmin will not display the traffic on the map page. Most GA aircraft don't have a heading input to their Garmin units. Also, other information available from ADS-B, for example target type (TISB or ADSB ), Ground or Airborne, N number, velocity vector, closure rate vector. are not available.
The original proving project for ADS-B was conducted mostly in Alaska. The project name was Capstone. A set of equipment was contracted for by the US government. It consisted of the MX20 and the GDL90 ADS-B transceiver. It included the TISB and FISB interfaces between the GDL90 and the MX20 and was in the public domain. When Garmin designed its support for the GDL88, GNS430W/530W and GTN, proprietary interfaces were used between these devices and Garmin abandoned the other interfaces. Since they were proprietary, other vendors such as Aspen, Avidyne, FreeFlight, NavWorx, and other non Garmin avionics companies decided to adopt the Capstone interface between their displays and ADS-B receiver systems. This made them potentially inter-operable between non Garmin vendors. So with a Garmin GNS or GTN, they don't support the Capstone interface, so it can't be used to interface with the other vendor's ADS-B products. With the Capstone interface, the competitors can use each other's displays and obtain the full ADS-B function for traffic and weather, but not with the Garmin GNS and GTN systems.
Since Garmin has so many GPS systems installed, the other vendors were able to provide traffic (only) using the older and less capable interface that I called the TCAD (or TAS) interface. This limits the display capabilities to the Garmin support for a TAS unit, for example number of targets, maximum scale, and data about the target. So they can say they support traffic on the GNS and GTN, but with limitations.
Garmin also supports the TIS interface (the one you called TIS-A). TIS is a mode S product and uses the data link capability that comes with mode S transponders. It has absolutely nothing to do with ADS-B. This interface is the crudest and has the least capability. I hate the -A because it is added to the acronym without having the "A" standing for anything. Maybe the "A" stands for Aint. It was made up to distinguish it from TIS-B or TIS-Aint.
The GNS430W/530W support for the GDL88 is also limited to using TIS symbology. The GTN has full support for the additional capabilities available with ADS-B, for example target specific information, direction and speed vectors either absolute or relative, ground or air status, surface traffic overlay on the airport map, potential for adding other applications, such as in trail spacing or enhanced visual separation (follow the target to the runway).