One thing I've noticed about the use of "rap" over/against "hip-hop" is that "rap" seems to be used to describe the genre most often by people who are NOT fans of the music, in an almost derogatory way. Usually, the way I've heard, it is used by people who have had little exposure to the genre outside of the context of the top 40 or the sort of videos you'd see on "Sucka Free" on MTV. I notice that most hysterical news broadcasts that bemoan the evils of gansta rap, especially since the time circa NWA released Straight Outta Compton and the LA riots and Rodney King was assaulted, use the term "rap" and are unaware of the broader "hip-hop" culture that "rap" is a part of.
(The term "hip-hop", on the other hand, seems to be used more respectfully and encompasses "rap" as one of its common aesthetic elements.)
The use of "rap" in this sort of derogatory way I mention sort of reminds me of the way people use "techno" who don't listen to electronic music and know little to nothing about it: they're mostly thinking of really cheesy trance or the stuff the guys from Night at the Roxbury bump in their car stereos.