First, what everybody else said. Second, my two cents:
Urban Fantasy is a predominantly urban setting + fantasy (typically modern/contemporary, but that's not required. Glen Cook's Garrett Files take place on a secondary world but are often classified as "Urban Fantasy"). It's no different than Epic Fantasy (world changing events + fantasy) or, say, Dystopian Science Fiction.
Paranormal Romance is romance centered on a HEA + fantasy, sometimes set in an urban setting, which then causes a bit of crossover. But where the purpose of a PNR story is to explore the characters' romantic relationship, set forth challenges, but eventually give them their happily ever after, a UF story's purpose isn't decided by it being an Urban Fantasy.
You could have the story be an epic quest to save the city, or it could be a struggle between different magical factions, or it could be solving a mystery, or it could be about a bunch of magical people trying to survive in the big, bad human world. All those stories would still likely be considered Urban Fantasy and, sure, some of them might have a romantic element, but it'd be the same way that an Epic Fantasy might have two characters fall in love.
Anyway, long story short, an Urban Fantasy doesn't need a romantic element. A Paranormal Romance, by definition, does. I'd consider "American Gods" and "A Madness of Angels" Urban Fantasy and though I haven't read it, the Goodreads blurb makes the "Fault Lines" trilogy sound Urban Fantasy.
@Sagana: I didn't really see where that agent said she will only read UF with romantic elements. I did see a lot of her saying she wanted something "different" that grabbed her attention and that she was sold on the storyteller's voice. True, that particular query had a romantic subplot, but I'd do more research on her before writing her off completely.