Gunnut69's good basic explanation of the differences between bluing and parkerizing are mostly correct, but with a few small changes.
The various forms of "bluing" are only rust-resistant, and not rust proof at all, as we have all seen active red rust through a beautiful blued surface.
So-called "parkerizing" is the phosphate coating that Gunut69 described and is a modification of the steel surface. Only ferrous (iron-based) metals can be phosphated. Parkerizing was the patented trademark of the Parker Metal Finishing Company prior to WWII. Since then, zinc and manganese phosphate finishes have been developed that are used extensively for military and industrial applications. They differ from the original iron phospate coatings in that the grain structure is finer and more complex, thus offering greatly improved corrosion resistance and ability to hold sealer top coats. Manganese phospate in particular is good for salt-spray resistance, and is standard for military weapons exposed to extremes of humidity and temperature changes. Phosphating is also commonly used as a base undercoat for finishes that add protection and beauty. Epoxy and powder coatings over phosphate are used by European military weapons makers such as H&K (GIAT), the former Soviet Union, and many NATO members. They are less well known in the US military because of the "traditional" phosphating of small arms since after WWI.
Other phospating applications include industrial machinery, automotive parts (body panels, engine components), and