The stories were basically written from whole cloth, based on fairly short mentions, in the four "later" books. From what I understand, they weren't even allowed to use Tolkien's notes.
I haven't encountered anything that has made me think this was a different "universe," but the general "feel" of the show is vastly different from Tolkien's writing.
For one thing, ol' J. R. R. was more than a little chauvinistic. Women didn't really play much of a part, in his writings, and when they did, they were fairly peripheral, or "objectified" (not necessarily in a sexual manner, but they were obvious stand-ins for some ideal).
I've been enjoying seeing Galadriel as an arrogant ass-kicker, but am a bit disappointed in a flower-sniffing Elrond.