The Scotch bright pad and toothpaste is about removing light rust from the barrel. Its not a lapping compound. You can use it to polish the lands of the barrel in a rifle, but if you have pits in the grooves, or serious pits in the lands, you need to cast an actual lap, and use laping compound to work on those.
Most guns can shoot okay with pits in the barrel. The pits do continue to hold debris, and require some soaking time to get them cleaned out between shootings, but they won't bother the accuracy of a PRB, where the patch, and not any lead, is what touches the bore.
To do a proper job of lapping a barrel, the breechplug should be remove, so that you can do a proper inspection of the entire barrel, and lap the full length of the barrel from the back end forward. To do lapping, you need a dedicated rod for that purpose, some way to melt and pour lead, and lapping compounds that are available from most auto supply stores.
If you have a badly rusted barrel, with lots of pits, and rough grooves, it probably will be cheaper to buy a new barrel than attempt to clean up the one you have. If the barrel is an antique, you may even want to consider having it lined with a new piece of steel tubing, rather than go to the time and expense required to bore out the barrel to another caliber, and then cut new grooves in the barrel.
I have used pearl drops toothpaste on a doubled wet patch on my cleaning jag to polish out a barrel that had rusted during storage. The metal turns the patch black. If the patch is tight enough, you can work the compound down into the grooves in addition to the lands, and polish the surface down a few 10 thousandths of an inch. The result will be a very smooth bore to load, and reload, fewer parts of the barrel that will hold residue very well, and usually better accuracy. The secret is to make sure that patch is tight moving up and down the barrel. When it does become easier, its time to put on more toothpaste, and even throw away the existing cleaning patches, and replace them with new ones, with new toothpaste. Alwets wet the cleaning patches, either with water or oil. The fluid keeps the toothpaste from merely sinking into the patch and away from the surface that is needed to rub against the steel barrel.
I also have tried JB Bore Cleaner, but this is more for simply polishing a bore, and not removing metal, or rust. It does do a good job of polishing, however. The company specifically disclaims the product as a lapping compound. It will remove light rust, but that is about it.
You can try a product called Flitz, which is sold as a chrome cleaner. It has chemicals and some fine grit in it that seems to help remove rust, and other stains mechanically from metal.