TOR is both a proxying service for standard websites (and to a lesser extent, other internet services), and also a way to access "hidden" websites that are exclusive to the TOR network, using the .onion pseudo-TLD.
Deep web is as I stated, content that can be accessed with a normal browser and some human input (such as a search term), but not by an automated crawler.
http://en.wikipedia.org/wiki/Deep_web