Melonite and Tenifer are a metal treating process which hardens the steel to a Rockwell Hardness similar to a diamond. Technically, it is not a "finish" although the end result is a finish.
So, the difference betwen the two is a common forum question and is always subject to a lot of debate and conjecture. There is also some bit that always comes up about the process being illegal to do in the U.S.
I asked HEFUSA the difference between the two. They should know since they are the U.S. subsidiary to the company that OWNS THE TRADEMARK to Tenifer and Melonite. This is what they responded (full name, phone #, and email removed):
"Dear remat457-
Tenifer® is a name used most often in other parts of the world; Melonite® is exclusive to North America . However, they are the same. Please let us know if we can help you further.
Michael *****
Manager, Sales & Service
HEF USA"
Don't believe me? Ask them yourself, or email me -- I will email the direct contact info.
Now, how the treatment works on different types of metal (stainless, etc) can be different. The resulting finish you put on can also be different. For example, S&W Melonite can be touched up with bluing pen, while Glock's Tenifer can not (and seems to be more scratch resistant).