Ive never heard of either of those. Im thinking maybe you heard someone get cleared to pushback and they either wanted to request a different turn, or to push into a different alley? Since you need clearance to go where you want to go in a Non-movement area, they may have gotten clearance to push in a certan direction but perhaps needed to de-ice or get over to another terminal. Hence requesting to get a push to turn in the opposite direction to prevent u-turning on a taxiway in the terminal environment.
Although, I'll be honest I have very little experience with using actual gates. So... feel free to correct me on this one guys.
~DAVE