Urban Fantasy is a genre that combines common fantasy conventions with a modern setting. It's a sub-genre in Speculative Fiction. Sometime people think it means that the whole story takes place in a large city- but that isn't the case, sometimes the city is a character itself (or say, a Park?) But most of the time large cities (the ones most people can name in a given state) are used because it is easier for the fantastical elements to hide themselves.
There is also a lot of cross-genre going on with Urban Fantasy so it becomes difficult to tell whether a work qualifies, but generally speaking Urban Fantasy is known for showing the impact of modern society on the fantasy elements included in it. There is also a lively debate of "when" Urban Fantasy is, so we don't run amok of Historical Fantasy, Alternate History and Future Fantasy. It's pretty complex- which means it's a lovely playground of possibility.
Because I write in both genres, I get asked where the differences are because it can be confusing when fantasy runs through both. I’ve had people confuse which genre my books fall into (Warriors of Luna- Urban Fantasy with some romance; The STEAM series- Paranormal Romance, but yes still werewolves). So here’s my basic break down of how I see the different genres.
Both are types of speculative fiction, involving fantasy elements (werewolves, vamps, other were-creatures, fairies, gods, etc.) in a real world setting and both tend to attract fantasy readers.
Urban fantasy takes place in a city – it’s necessary to have it in an urban space. Paranormal Romances don’t have that limitation.
Urban fantasy uses fantasy tropes: good versus evil, saving the world, etc. Main characters live in a city and have or find out they have supernatural something going on. It may or may not have a romance element—plenty do, as a sub plot.
Paranormal romance has the main goal for the characters to fall in love. The journey of falling in love, some kind of drama that threatens the love (such as finding out your boyfriend is a demon) and then the character ending up together. Paranormal romance, like regular romance, can cover the whole genre- so there is a ton of variety. Paranormal romance uses romance tropes: HEA (Happily Ever After) or HFN (Happily For Now), that urban fantasy doesn’t have to follow.
Urban fantasy usually has a more stylized voice to match the action or tension— sometimes landing it in horror. Horror isn’t the case for my novels, even though there is violence. Supernaturals can be good, bad or the gamut.
Paranormal Romance has an easier casual voice, with violence being a nice gauzy event off page. The supernatural are more alluring and intriguing.
Of course, you can and will get different answers from different authors. This is just my take.