Let us say I have 2 modules. First module gives a differential signal output on a pair of wires while the second module takes the differential signal input.
When I connect the differential signal wires between the modules do I need to connect the GNDs of the two modules together also?
In general, yes you do need to connect a common ground between these modules.
The receiver hardware on the 'input' module will have a 'maximum common-mode' voltage spec for its inputs which you need to ensure is not exceeded, and this voltage is measured with reference to ground.
Of you don't connect Ground between the 2 modules you don't know what this common-mode voltage will be potentially resulting in the receiving module incorrectly interpreting the differential signal and/or suffering some damage.
