There is a difference.
But sometimes you're a jogger, sometimes a runner.
Most of my runs that I do I'm a jogger, easy aerobic effort, not pushing the body too hard.
When you're a runner, you're pushing the body to run fast, but not hard, it should hurt, but not too badly.
When you're a racer, it should hurt like hell!, but you keep your head around you.
When you're a sprinter you give it everything you have with no thought for caution.
I've never been offended when someone calls me a jogger, I know that most of the time I am, there's very few runners in the world who aren't also joggers, and those that aren't also joggers end up being not very good or injured.
In reference to the question, the first time you think " what could I do to be a better runner" for the sake of running, not fitness, that's when you're a real runner using the standard definitions people use of runner and jogger.