Zoar: Both processes involve oxidizing steel. Browning takes place at a lower temperature. Boiling water is higher, and uses the water molecule to change the brown to blue. Its a dark blue/ almost blue black color, but will fade with handling, somewhat, unless you put oil on the hot barrel to burn the colors into the pores of the steel. Dipping a barrel into a tank of boiling water for 10 minutes or so raises the temperature of the barrel high enough to change those colors to Blue/black.
When you remove the steel from the boiling water, spray the barrel or parts with wD40- both an oil, and a water displacing component in that-- and let the barrel cool down to room temperature slowly.
I found that leaving the barrel dripping wet with oil overnight gave me the deepest and darkest color.
I also heat the barrel up much hotter than 212 degrees F., the boiling temperature of water. The hotter the barrel, when I spray it down with WD-40, the deeper the color goes into the metal, so that the blue finish lasts much longer with normal handling. I use a propane torch, on the blued barrel to heat it hotter, before spraying it with the oil.