I've had this problem before. It only happens to me once in a while, and I still haven't figured out what exactly the cause is. First of all, those boxes you're looking at are for Polygons and Objects - the one with the dots moves the selection mode to Polygons for the selected Object, and the one without dots selects different Objects, such as the whole fire engine. Try making sure that when you move from one set of polygons to another to UV map, use Select > None and click a few times to make sure all the old ones are deselected. It looks like when you selected the polygons for the hose bed of the truck, the ones from the right side of the truck were still selected and so those got re-mapped as well. If that doesn't work, then the one thing that I know will work temporarily (but is time consuming) is to save, exit, and restart each time you finish mapping a certain part. That makes absolutely sure that no other parts of the engine could be selected, since you've essentially reset the program. Usually the first fix works for me but if it doesn't then you can use the second one until you can figure out what exactly the problem is. Good luck