I was trying to use what I thought was a 220V receptacle at work but the
voltage was only 208V. When measuring, I see 120V between each hot and
neutral but only 208 V between the hot leads.

Am I really looking at two legs of a three phase Wye connected branch
circuit as opposed to a 220V single phase supply (common in residential).
Is this a common practice in commercial buildings? Should the round twist
lock style plug be telling me something? (nothing like a range or dryer
plug)

Does that sound right or do I need to open the panel and trace it back to
figure it out. These receptacles are leftover from the previous tenant so
their original purpose is lost to me. They are protected by a regular two
pole breaker (with tie bar).