My reputation isn't high enough to up vote nor leave a comment apparently, but I support @Chris Sunami's answer to this question.
I would also add some fuel to your fire by adding to your question the terms "right" and "correct". How do we determine the difference between truth, factual, right and correct? They all overlap one another with their meaning and if we tried to define them separately we would most likely end up using shared terms to do so.
Essentially, when confronted with a definition question such as this, my personal best practice is to remember that no term can be defined concretely (although we may and ought to try to get as close as possible) thus leaving a fair amount of "give and take" in any definition we decide to use. After all, using words to define words will always put us in a tail-chasing conundrum after enough discussion.
So the solution, as I see it, is to be as clear as possible within whatever context we're using our terms, but to simultaneously keep in mind that when another person uses those same terms, their definitions may vary. Notice the quote from Bertrand Russell that @George Chan placed in his response. Russell defines these terms for his audience in order to alleviate confusion and place everyone on the same page, as it were.
To answer your question directly, I suggest defining the difference between truth and fact by stating that qualitative measurements of reality lead to truths while quantitative measurements lead to facts.