You definitely do NOT have sway.
There are not "multiple definitions" for sway. Sway is not a momentary bobble of the trailer hitting uneven road. Sway is not even the effect you feel from a passing bus or semi.
Sway is an ACTUAL loss of control, that you cannot recover from without extraordinary effort. Sway does not cure itself. Sway does not disappear as the distance between you and the semi increases. Sway always gets worse if left uncorrected, never better as time passes. You either hit those trailer brakes or you end up backwards in the ditch.
What you have is an adjustment issue. Perhaps not enough weight on the front axle of the truck. Perhaps your sway bar system is not being used correctly.