Neither the implement in Tractor Man's picture nor the one in the Ebay illustration can be anything to do with shotgun barrels – they are far too short. I have a shotgun bore micrometer, and it has a reach of over 16 inches, so that it can be inserted through either the chamber or the muzzle to measure anywhere along a 32-inch barrel. In addition, I don't think the Ebay implement could be anything to do with dent removal in any kind of tube. I think (guessing) that, rather than forcing the dent out, it would cause a bulge on the opposite side. Shotgun dent removal tools I have seen spread the load over quite a length of the opposite wall of the tube. Some are mechanical, and others hydraulic. If you Google for "shotgun barrel dent removal tool" and look at the pictures, you will see what I mean. I think it's just a tube expander, as Peter suggests, possibly for use by plumbers. As for Tractor Man's mystery tool, I haven't a clue.