Howard Shore was working on the score, then left over "differences" with the director. The score is now credited to one guy with "additional music" and "ambient music" credited to another guy.
What is "ambient music" - is it the same thing as "source music"? 
You mean, is it "diagetic" vs. "non-diagetic"?
I think "Yes" is your answer.
Normally, I think of "ambient" in terms of "sounds", such as the sound of a waterfall, or rain, or the sound of a train chugging down tracks, etc. While this can be captured on film, too many other sounds interfere, so they are more often added in later by the Foley team. I think "ambient music" might refer to the music that can be heard in any given location...such as a mall or an elevator or store where music plays over the store's system...part of the "ambience" of the locale.
And, of course, this is also called "source" music, such as music coming over a radio or music that an orchestra plays in a nightclub sequence, etc. In "King Kong," it could mean the music the natives play during their rites/rituals. It could be the music of a marching band during a parade. Someone credited for "ambient music" need not have written it...but might have secured the rights for it, whatever it is.
This type of music in movies is often referred to as "diagetic", while the underscore (the film's original music that some of us are always aware of but many are not unless there's a pretty theme or song, such as Lara's Theme or Moon River) is "non-diagetic." (In the case of Moon River, it's diagetic only when Audrey sings it on camera...all the orchestral occurrences during the film are non-diagetic).
Lots of discussion -- most of which fries my brain -- has taken up bandwidth in various discussion forums on this topic. Folks who like to discuss this will most like say my explanation is very simplistic because there are so many variables "they" like to ponder and argue. But I think I've presented the gist of it...in simple terms.
