Well, in the case of WSB here are the calls:
WSB 750 AM
WSB-FM 98.5 FM
WSB-TV Analog Channel 2
WSB-DT Digital Channel 39 (I think)
In the old days AM stations never had to put AM in the calls. Nowadays, whichever station has the calls first does not have to put an extension.
To address the DT issue, I am assuming that since the calls are in the FCC database and licenses are issued with DT as the extension, then DT will stay. The last part is a guess and maybe some of the engineer types can give us more insight.