1.) Urge, is to have the desire to do something.
2.) Convince, is something you have to prove to someone.
For example:
1. ) I have the urge to finish my homework, so I can go outside with friends and play.
2. ) Last week, I wanted my friend to see a movie with me, it was suppose to be a really good movie. My friend did not want to see it, because they thought it might be boring, but I convinced them to see it and they really liked it.