They are the two different formats of blank DVDs for use with PC's. Many PC drives will only play or burn one format, and many stand alone DVD players will only play movies on one format or the other. Many newer PC drives and players will work with both, but it is something you need to be aware of, that some discs may not work for you.
It is similar to the old VHS vs Betamax debate. There were two formats and eventually one of them won. At the moment it is isn't really possible to say one DVD format is better than the other, or which will become more dominant, they are both still popular at the moment. Personally I think DVD-R is the way to go, but both are strong at the moment.
Hope this helps? If you have any more questions - just post or PM me.