In several circumstances the two terms have the same meaning; the distinction I see: real facts are also true, as they describe what is happening in reality, i.e. in the world; true is an adjective that finds its proper place also for abstract assertions, like the truth of a belief, of a Mathematical proof, of a Physical theory. Sometimes 'real' is used to mean if the other person has 'true' feelings towards us, like in the question: 'are you for real ?'