I didn't really think there was one, except that some contemporary fantasy does take place out in the country (Megan Lindholm's Cloven Hooves is set mostly in Alaska, with forays into farm country).
There is a specific subgenre of the subgenre which seems to involve street kids, bouncers, buskers, or other streetwise, punky folk, and elves. (Examples range from Mercedes Lackey-and-various-co-author's Bedlam's Bard and SERRAted Edge series', the Bordertown shared world, and Emma Bull's War for the Oaks). Maybe this is what people mean when they differentiate Urban fantasy form Contemporary fantasy in general.