Hip-Hop is the name of the culture. It includes DJ'ing (the beat, the music), B-Boying (the dance, also known as breakin), Graffiti art (muralism, tags,) and Rap (the word, the voice). Rapping is what an emcee (mc, lyricist) does when he orates to the beat. Many schools of thought include the 5th element of knowledge, which in an overstanding of self, community, history, and divine purpose.
http://wiki.answers.com/Q/What_is_the_difference_between_Rap_and_Hip-Hop
http://blogcritics.org/archives/2006/10/19/071848.php