Rap is the story telling medium of Hip Hop. Hip Hop is a style of music that can encompass everything from RnB to Soul to even some Electronic Music. Rap is Hip Hop that has a specific emphasis on lyricism, meaning, and narrative. All Rap has elements of Hip Hop, but all Hip Hop does not have elements of Rap. Obviously this is all subjective to a certain degree.
To answer your question, Jay-Z's MCHG is probably more Hip Hop than Rap, while old school Kanye is mos(t) def(initely) Rap. However, unless you plan on getting into conversations like this in the future I really wouldn't worry about the difference.
Ok, this makes sense. I pretty much invariably call the hip-hop/rap music I listen to "hip-hop". De La Soul? Hip-hop. Jay-Z? Hip-hop. The Roots? Hip-hop. Run DMC? Hip-hop.
To answer your question, Jay-Z's MCHG is probably more Hip Hop than Rap, while old school Kanye is mos(t) def(initely) Rap. However, unless you plan on getting into conversations like this in the future I really wouldn't worry about the difference.