Rap Vs. Hip-Hop:
Rap is a form of music that stemmed from hip-hop culture. Hip hop is a lifestyle with its own lingo, dress code, etc. In the words of KRS-One, "hip-hop is something you live, rap is something you do."
Hip-hop is a form of popular music that's comprised mainly of emceeing and deejaying. The other two components that complete the four elements of hip-hop are graffiti and breakdancing. As hip-hop evolves into big business, the four elements (emceeing, deejaying, graffiti, and breakdancing) are constantly being merged with others like clothing trends, slang, and general mindset.
Hip-Hop Started in the Bronx:
A product of cross-cultural integration, rap is deeply rooted within ancient African culture and oral tradition. Hip-hop is believed to have originated in the Bronx by a Jamaican DJ named Kool Herc. Herc's style of deejaying involved reciting rhymes over instrumentals. At house parties, Herc would rap with the microphone, using a myriad of in-house references. Duplicates of Herc's house parties soon drifted through Brooklyn, Manhattan. Herc and other block party DJs helped spread the message of hip-hop around town and spawned tons of followers.
Some of the earliest rap songs ever recorded include "King Tim III (Personality Jock)" by Fatback Band and "Rapper’s Delight" by the Sugarhill Gang. The latter reached the #36 spot on the Billboard charts (a huge feat by 1970's standards), thus demonstrating hip-hop's ability to draw commercial appeal.
Hip-Hop As a Melting Pot:
Hip-hop as a musical melting pot is still evolving. It has become more eclectic, borrowing from soul, jazz and live instrumentations with the likes of De La Soul, A Tribe Called Quest, and most recently Kanye West championing the ‘soulful rap’ movement.