it's different if the whole texture is wrapped around the object or only a part of it. i guess that your texture is completely gizmo-mapped, right? then only the seam, where the two end meet, should move.
try a object, like the streetlamp from the res bridge, and you'll see that, when you change te offset in the unwrap window, the whole texture is moved. you'll see parts of the asphalt at the lamp, etc. cos the lamp is only one part of the big bridge texture.
btw. has anyone figured out what the "weight"boxes in the unwrap toolbox are about?