If you Nitre Blue but run the temp of the Nitre salts up to 830/850F,,you will get the (near) same deep blue/black color as that of charcoal blueing.
Actually the color will look closer to that done with the American Gas Furnace rotary furnace method.
True Charcoal blue has a slightly 'bluer' tone. But steel type, polish and who's doing the actual bluing all come into play just as in any finishing work.

Don't take the temp much above 850F.
Don't get it near 900F or you'll get a grey color on the parts and that'll be the end of that for the parts as far as coloring them.
You'll have to pull them out, allow to cool. Then re-polish and start again.
That grey color happens just before the steel starts to turn red (heat). That red heat point is right around or at 900F I figure from the mistakes I've made.!

I've mentioned the use of the high-temp Nitre salts a few times, maybe here and other Forums. Never got much response about it.

Like the lower temp Nitre Bluing done at the 650F range, the higher the polish,,the brighter the 'Blue'.
Don't be shy about a high polish. But a sloppy polish won't be hidden by this blue or any other.

This process can be incredibly dangerous as you now have a big container of Sodium Nitrate at 850F and you must keep it at that temp of 850F through the entire bluing time.
Keep any moisture far away,,just like when casting lead. Very explosive reaction.
Safety measures/clothing/eye protection. Even then this stuff if it ends up on you will burn through most anything you can wear and then burn down into your skin.
Anything in your eye,,your eye is gone.

It's hotter than lead is during bullet casting & the quantity can be a lot more when you want to immerse long parts like straight grip trigger guards and bolt rifle triggerguard/magazines completely in it. The parts must not touch the sides of the container. They can hang from wire.

It can take a big heat source to get you there and keep you there.

Smaller parts like latches, sights, screws, ect can be more easily & safely done in a smaller container.
I used to do some restoration parts that way after using the same bath at a lower temp to either spring temper and/or common Nitre Blue some parts that I could do at the same time.