They are used pretty interchangeably (in Canada, anyways), but generally jogging is slower than running. Going for a 'jog' is more casual than going for a 'run'. You would never call a competitive athlete a 'jogger', they would definitely be a 'runner'. I hope this helps. 

I agree with Emma, and will add that joggers usually have more vertical motion than runners. In other words, runners are usually smoother.

Agree with what everyone here has said.  I'd also add that it's more common to say "run" versus "jog" when talking about exercise, especially among younger people.  I am a runner, and I never say "I'm going to go for a jog".  It's probably because it sounds more "serious".  If you look at the product websites of companies that make running gear (Nike, Adidas, etc.) I would say 99.9% of the time they say "run" in their marketing messages.

Runners take the whole thing a lot more seriously than joggers. It's kind of like the difference between someone who enjoys karaoke, and someone who considers themself a "singer."

Thank you very much!