Facebook perfectly fits the original definition of the term [1], but unfortunately media confusion has turned it into a synonym for Tor and hidden services.

[1] https://en.wikipedia.org/wiki/Deep_web_%28search%29

Are you not thinking of "dark web"? I see that a lot, but I've not seen "deep web" used by the media at all (though I won't deny that the media misusing technical words is entirely believable...)

"Dark Web" is indeed the proper term, but it's been conflated with "Deep Web" in the media. See the section "Terminology conflation" in that Wikipedia article.