I know that one could use either the term rap or hiphop to describe any of the types of songs that we are talking about, but I personally think that there actually is a difference between rap and hiphop.
Hip-hop is more what you would find at a dance club, and is more likely to be enjoyed by women. It usually contains some reference to shaking ones ass if they are a female. A good example of a song that I would call pure hiphop would be hey ya by Outkast.
Rap is more "hardcore" I suppose you could say. Generally more enjoyed by guys, although it usually doesn't sell as many records as hip-hop does. Guys are more likely to enjoy rap over hip-hop. Rap contains more verses of pure rap then hip-hop would, and usually contains less in the way of a chorus. An example of a rap song might be something by Tupac, or Slob on my Knob by Three Six Mafia.
Those are the definitions I use, at least. Of course some songs are in the middle of these two types.