My two cents:

GPS ID - Officially Garmin calls this Unit ID.

Map ID - There are two different definitions of this ID which lead to confusions. Tools like JetMouse keygen consider the Map ID the same as Family ID (FID). Whereas tools like GMapTool think Map ID as the unique ID of a map tile. There is no right or wrong. You can call an ID whatever you want because Garmin never publishes the defintion of an internal ID.

Personally, I will refer Map ID as MapSource Product ID, and is the same as FID. For the unique ID of a map tile, I will call it Map Tile ID, or Tile ID (TID) for short.