All rap means is music where the lyrics are spoken or chanted to a beat as opposed to sung. Rapping describes the actual act of speaking the lyrics to a song, a common feature in hip hop music. Hip hop originally referred to the entire culture involving rapping, DJing, graffiti, etc.
Hip hop music often contains rapping, DJing, sampling, etc. and the term “rap music” is often used interchangeably with “hip hop music”.