Let me make it easier
Sway: Side to side rocking of the body,, Tilts left, then right, then left (or the other way around) think of fans swaying in time with the music at a "We Love The World" concert.
WAG: side to side wagging of the "Tail" Think dog,, In this act the body is moving side to side over the axles.. Often the front moves left while the rear moves right, then they swap over and over (Again you can start in the other direction).. Pan-hard bars or Track Bars deal with this.. ONE (usually the rear, though I put on a front) will greatly reduce it,, TWO (One front and one rear) will stop it and I mean DEAD. 100$ elimination.. NOTE: Front trac bar not needed on vehicles with STRUT suspension or with independent front suspension (Only on vehicles with solid front axle) same applies to rear. but motor homes made that way.. DO NOT exist.
Steering stablizer... This device helps to keep you on the straight and however wide the lane is. There are several types but the idea is to hold the wheels in the "Straight ahead" position. Mine is a Blue Ox Tru-Center.