Patina can mean different things to different people. According to Merriam-Webster, patina is “a usually green film formed naturally on copper and bronze by long exposure or artificially (as by acids) and often valued aesthetically for its color” or “a surface appearance of something grown beautiful especially with age or use.” Some folks really like the look of an aged, well-used surface, but others don’t. Wood and leather tend to develop “character” as they are used and weathered by the elements. Copper and bronze tend to develop a green film over time, and steel or iron will rust. These forms of oxidation can act as a protective layer on metals. However, it does change the appearance.
The above photo is of an old Barlow pocket knife showing some patina on the steel parts.
Bluing on rifle, shotgun, and pistol barrels is a controlled chemical reaction on the surface of these metals to create that protective layer. This process is essentially converting the red oxide (rust) into a black oxide that takes on a black/blue color. So, the intentional rust will protect the piece of metal over time. While this doesn’t make the item impervious to rust or corrosion, it does help.
There are other ways to force a patina. They make bluing kits you can use at home. You can use vinegar, mustard, coffee, various acids, and other common products to achieve this effect. However, most carbon steels will develop their own patina over time with use. Often time, even with diligent care a knife or tool will change appearance. Sometimes a patina can be cleaned off with sandpaper or steel wool if it’s just not your thing. However, extensive rust growth can be corrosive to steels. This leads to pitting, discoloration, and will damage the steel over time.
Maintaining a coat of wax or oil can help prevent rust and patina. Proper care of your knife or tool will ensure it last a long time, and looks its best too. Although, some folks don’t mind the look of age on a blade and it is ultimately a preference of the individual. Even some stainless steels will develop patina or rust if severely neglected. After all, stainless does not make it indestructible, but it should "stain less" easily.
Personally, I try to prolong patina development on carbon steel as long as I can with proper care. However, I do have some knives and tools that have earned their patinas the hard way with time. There are many tutorials on Youtube about forced patinas if you are interested though. Remember to use caution and safety when handling corrosive chemicals if you pursue this approach.