From some source I saved, likely stored here somewhere from a long thread on various metal finishing.

More on Blueing
Date: Nov 21, 19:36
From: Oscar Gaddy
C-man
All true blueing processes for steel create iron oxide films in one way or another. The thinnest are the temper colors or temper blue which gives the azure blue color that you previously mentioned. The films that produce this color are only about one-half weavelength thick for red light or about 30 millionths of an inch thick. The thickness that produces blue black colored niter or charcoal blue (including carbona blue) is about double that, but the increased thickness makes a big difference in durability of the film and the finish. Slightly increased thickness yields the true black colors that can be obtained with both charcoal and niter blueing.

As far as which method is correct for restoration of older doubles, I do not think it makes any difference if the color that was obtained at the factory is reproduced on the refinished part. All processes produce identical films of iron oxide. For example, the original finish on Parker triggerguards was a deep blue-black. This can be obtained by any of the three processes. As you pointed out, it would definitely be wrong to refinish a Parker triggerguard with the dark azure blue temper color or "Nitre Blue" as Brownell calls it.

I believe that Roy Gunther and his colleagues have found in their research that Parker used the niter blue process that produced the deep dark blue-black finish on their triggerguards and skeleton buttplates. I can't help but believe that all of the major American gunmakers used essentially the same processes for the finishing of their guns with some indivudual nuances such as differences in the casehardening colors. The key technical people such as plant superintendents surely communicated a great deal and in some cases moved around from company to company. I believe that , at least before about 1920, all of the gunmakers used niter blueing or a very similar process for small parts such as triggerguards. Old style charcoal blueing is much more difficult to do than niter blueing. They may have switched to the carbona blue process after it became available in about this time frame and it is very probable that Remington used either this process or hot salt blueing for certain parts on the Parkers manufactured in Ilion, NY.
Oscar