Is there an official definition for "rural"? Most people here just seem to define it as socially conservative yokel. For example, just outside Iowa City, there is a town called Kalona in Washington County. It's very Republican, it's only about 2,500 people, etc., and it fits the stereotypical "rural" fit for things like our maps and such. However, if you went there (as we often do, because it has a GREAT restaurant and a cool brewery), you would not think that the people living there were different culturally than people who live in Iowa City, even if they are politically. It's not this foreign planet.
There is, on the whole, less ethnic diversity in rural America. Rural Americans are more rooted and grounded in the place they're at; they're more likely to have been their for generations and more likely to have LOTS of family living locally.
I may notice these things a lot because I live in Florida, in a diverse place where folks ask "Where are you from?" in introducing yourself. And the answer is usually someplace other than where you're living. I go to Jackson, OH, a town on the edge of Appalachia in Southern Ohio, to visit my grandchildren, and family there is a big deal. Urban America, for the most part, is a place where this rootedness has broken down, and rural Americans don't want that to happen to them. Indeed, there is much of rural America that would be in worse shape if family structure there had taken a bigger hit than it has over the years. Family has been a big part in getting a lot of small town and rural folks through the hard economic times that came with the exporting of their jobs.
I asked a smart lady I was sitting next to on a plane, who grew up in rural Vermont, in a place now beset by all sorts of issues, just why she thought so many that lived there did not leave. She said, it is because of the extended family. It does act as a sort of social safety net, and many perceive it as essential to their survival, and it would terrify them to abandon it for the social anomie of a place where they have no extended family.