I have been finishing firearms on and off for many years, and have experience with caustic hot blueing, Parkerizing, and black oxide. A brief description of each process will help since they all are very different.
This is a phosphating process, where a relatively thick porous salt of iron, zinc, or manganese phosphate is formed on the surface of iron or carbon steel. A few alloys of stainless steel will except this process, but not too well. The color in its natural state is various shades of grey, but the thicker variants (like manganese phosphate) can be dyed black or another dark color. The porous nature allows it to soak up oil or some other preservative, and this greatly improves it corrosion resistance. The thick porous nature makes for a rougher finish, so it never looks as good on firearms as blueing. Phosphating is much simpler and easier to apply than hot caustic blueing, its a great process to start with if you are new to this.
Black oxide is an oxidation process, basically its controlled rusting of the iron or carbon steel its applied to. This dark grey or black "rust" forms a very thin layer on the steel, but because of the low temperatures and less caustic nature it doesn't penetrate the steel very much. This makes it both less durable and less even a finish than hot caustic blueing or Parkerizing.
Hot caustic blueing is also a controlled "rusting" process. In spite of the name it isn't blue, its black. When applied to a highly polished surface the way it reflects light makes it look blue or blue-black. On a matte surface its totally black. The major differences between this and black oxide are its very caustic and corrosive nature, and the high and critical operating temperature it requires. However these requirements also make it vastly superior to any black oxide process done at lower temperatures.
Its not well known that totally clean steel will start to rust within seconds of being exposed to air, the humidity provides the moisture, it needs very little. This rust is microscopic and invisible to the naked eye, but its there. This microscopic rust is what makes it difficult to get an even finish on a large area of steel. Black oxide or its relative "cold blueing" is partially blocked by the rust, the blocking also contributes to why it won't penetrate as well as caustic hot blueing, so its less durable.
Caustic hot blueing is applied at 292 degrees F.; +/- 5 deg. F., the actual numbers will very with the formulation of the blueing salts. The high temperature and highly caustic nature allow it to quickly dissolve the microscopic rust, and penetrate the steel deeply. This is why the finish can be totally uniform even on large surfaces. The deep penetration is why its much more durable than black oxide. This is nasty stuff however, it will corrode any ferrous metal in close proximity, and handling it requires great care, it can cause very serious chemical burns. If the temperature is not accurately held, reddish or brownish spots will appear, ruining it. It will quickly dissolve aluminum, which contaminates the salts making them useless.
In spite of being dangerous and critical to apply, absolutely nothing can approach the outstanding finish it provides, which is why it is dominant on firearms and other high value ferrous mechanisms.