You need to use layers and masks, layers are where the objects are detected for collisions and masks where they look for collision.
The idea is to match layer and mask of the monitored and monitoring nodes (to use Area wording)
If your "world" is on layer 1, the special bodies need mask on 1 to detect it.
But you don't want theese bodies detect each other, so they can't be on layer 1, remove all the layers on them.
Now, if your game world or specific parts of it need to detect the special bodies, add layer on 2 to the bodies and mask on 2 to the detecting nodes too.
With 1 and 2 I mean the checkboxes on the inspector, look the docs to see how to use the methods.
ps: as of Godot 2.1.2, the 3D version, KinematicBody, is not using masks, just layers, and Area2D may look for both in some cases, do some tests first.