Lets say you have CompA that contains LayerA and LayerB, and CompB with LayerA and LayerB.
If you use the "Copy with property links" to grab the position of CompA/LayerA and paste it onto CompB/LayerB it will link to CompA/LayerA. Its an absolute link.
If you use "Copy with relative property links" to grab the position of CompA/LayerA and paste it onto CompB/LayerB - it will instead link to CompB/LayerA. Its relative to the comp you are pasting it in so it will look for a layer called LayerA within the current comp, and return an error if one does not exist. If you look at the expression it writes, you will see it reference "thisComp" rather than the name of the original comp you copied from.