There's no difference, just different ways of saying it. It's like saying 3 feet or a yard.
Melonite is a treatment to the metal itself which makes it harder and more slick. It is NOT a coating that is applied on top that can wear off like chrome lining for barrels or nickel boron for bcg's. If done properly, it can be on par with CHF/CL barrels but the advantage to melonite/nitride is that it doesn't cost quite as much.
Melonite is extremely corrosion resistant and was starting to become very popular with the 5.45 surplus crowd until the ban was imposed.
Melonite is extremely hard so it extends the barrel life by great lengths. This in turn has made competition shooters very happy since stainless barrels are popular but have a shorter life span since stainless is softer than 4140 or 4150. Another advantage to the hardness is that the finish is a lot harder to scuff, scratch, or knick.
Because melonite is so slick, you can usually gain a few fps compared to the exact same barrel that is either not treated or the exact same barrel that has been chrome lined.
Be wary of lower tier companies that offer melonite barrels. Some of them have been known to take short cuts in the manufacturing/assembly process. Rather than having the barrel and barrel extension treated separately, they will install the barrel extension to the barrel and have them treated together. This causes the barrel extension to lose it's previous torque value (mil-spec 150 ft lbs) to such a degree that it isn't uncommon for the barrel extension to come lose when trying to do something as common as removing a flash hider.
What's amazing about melonite is that it isn't specific to one type of steel. You can get it on barrels made of stainless, 4140, 4150 or bcg's made with 8620, 9310, C158, tool steel, S7, etc.
As long as you are buying from a quality manufacturer, there should be no worries, only the satisfaction of knowing that what you are buying will have an extended service life and require less elbow grease during cleaning. Here's a list of common names that you'll see the top companies use which all mean the same thing.
Black Nitride
Ferritic Nitrocarburizing
Melonite
Salt bath nitride
QCP
Tenifer
Hope that helps.