OK What are those smartphone car adapters and what do they do?

Basically, they are interpretation devices.  

Many vehicles have external CD changers (or Satellite Radio modules) and they plug into a port or socket on the back of a factory car stereo to operate.  Even if it doesn't have a CD changer, it most likely has the port (for the dealer to install a CD changer if you wanted one as an optional accessory).

These kits make use of that port by enabling communication between the car stereo and your smartphone. 

In other words, they make your car stereo think that your smartphone is a CD changer!  But better!  

What are the many GROM Audio Kits and what do they do? 

Here is a kit comparison table

Want to know what kits are available for your vehicle?

Here is an application guide

Does the connector at the back of your stereo fit the kit harness?

Harness compatibility chart