The term "Express" was originally applied to high velocity black powder rifles. I think Hollands first used it, in the same way that "Magnum" is used. (By the way "Magnum" isn't new either. Hollands used it to describe .375 as long ago as 1912! It derives from a magnum of wine having twice the capacity as a standard bottle).

When Nitro powders began replacing BP, "Nitro" was added to "Express" to differentiate it from BP Express. I believe Rigby produced the first NE cartridge - the .450 3 1/4"

As far as I know, no one owns the term.