In most recent songs, rap music had developed and changed from a "thug" trend to a party and materialism type of genre. Rock, on the other hand, can be argued to have stayed over the majority of its 40+ years. .
Rock has been about sex, drugs, loss, love and more. That's not to say rap doesn't share any of these topics, but over the years, rap has change a lot in the messages that are supposed to be sent with each song. Take a recent song by Nicki Minaj- "Only" which uses a lot of vulgarity, speaks of all the fame and glory she, Lil Wayne, Drake, and Chris Brown have achieved, and how "only" if you're rich, famous men or promiscuous, sexy women like them can you be "friends with them". Now, compare that to the song "Do I Wanna Know" from the Arctic Monkeys, speaking about an obsessive lover who is paranoid about the state of his relationship. Those two are more recent song that show how both genres speak of different topics in their song. .
On the stereotypical side of these genres, Rock has been portrayed as a "white" genre of music while Rap has been portrayed as a "black" genre because of the fan base and races of artists of both genres. I totally disagree with this statement; you don't have "been" either or to enjoy the songs, if you like them, listen to them, you shouldn't be characterized because you like something. One main difference is that both these genres were started in different time periods. Rock started in the mid to late 1960s-1970s. Rock evolved from "rock 'n roll", and yes, they are different. On the other hand, Rap started in the early to mid 1990's and it evolved from "Hip-Hop". Rap is somewhat still considered "new" by a lot of people because it's only been around for about 20 years while rock is considered classic in the eyes of many people.
Apart from the many differences these two genres have, they both are very similar to each other in their own ways.