If you examine the rust spots closely with a good magnifying glass, you will see little " flowers" of rust, rising out of a much smaller "spots".
To remove these flowers of rust, I first cover the entire barrel with a good motor oil, to protect the non-rusty areas of the barrel and finish from being scratched by the iron oxide( rust). Then use a coarse cloth- a tack rag works, but so does a burlap sack, canvas, etc.--- dipped in the motor oil, to LIGHTLY rub the rust, on spot or area at a time. The Flower breaks off at the surface of the metal. You want to clean the rag, or use a new one, so you don't load the rag up with iron oxide crystals, which will scratch the finish. I have used 4 0 Steel wool, soaked in motor oil to burnish off rust on a barrel, but I know what a LIGHT stroke means. Not everyone does. I also know how to use coarse cloths to accomplish the same thing. This comes with experience.
Just make sure you don't ever remove the motor oil from the barrel, until you are confident that ALL the rust spots have been removed, and you are now ready to clean the barrel of all the oil. I use alcohol to thin, and remove the oil, wiping it on with a cloth that absorbs the oils, too. Cleaning patches, or flannel shirts, do well for this task.
What you will have left will be LIttle spots in the metal- holes- that look like someone had a fine needle they poked into the barrel--- where there were much larger "flowers" of rust. You job just got smaller.
Blued barrels are reblued, but I heat the barrel up with my propane torch FIRST, and apply the bluing compounds while the barrel is very hot- about 350 degrees. Browned barrels can be touched up similarly using browning solutions on a heated barrel. When I finish with the acid solutions, I first rinse them thoroughly, then use alcohol to remove any oil residue that may have gotten on the metal. Then I heat the barrel up Again, and spray it with a good oil- like WD30, or Rem Oil, so that the oil burns off, like steam, and leaves a much darker color to the finish. I let the oil on the surface stay there while the barrel cools to air temperature, and leave it like that for 24 hours. The delay seems to help make the finish darker, and more even. The heating of the barrel seems to burn part of the oil, adding some carbon in the pores of the steel barrel.
Now with use, and cleaning, both a blued barrel, and a browned barrel will get lighter in color. That is just the nature of the beast. But, generally, if you heat the barrel before applying the solutions to blue or brown the barrel, the finish will last for more than 10 years of strong use. If you apply the acids to a cold barrel( ie. " cold blue") I find that the finish is rubbing off within a year or so, from using the gun.