grounding - Ground Loop for balanced connection

Different articles and tutorials covers somewhat contradictory information about ground loop.

For a balanced connection (differential), the return path is the other differential pair, however sometimes it is recommended to send the ground wire as well. This is to assure that the difference between Ground A and Ground B is within the common mode range of the receiver.

However, some other times, it is mentioned that even for a balanced (differential) connection, the ground wire could cause some problem. For such cases, it is recommended to use some sort of ground lift adapter along the path of the ground wire to eliminate the ground loop. Then if that is the case, then why do we even need the ground wire for a differential pair at the first place?

Even if there is potential difference between unit-A and unit-B, connecting that ground wire will still generate a ground loop and will cause the noise (hum), rather than solving the common mode range of the receiver!

Then how does sending the ground wire work? When do we use it, and when do we avoid using it for a differential pair?