If something is true, that generally means it is factual or correct. But, if something is real, that usually means it is authentic or genuine.
However, real is sometimes also used to mean true, but that is more of a slang usage, not formal usage. For example, if you were out at a social event talking to friends and you made a statement that someone found surprising, they may ask you, "Is that for real?" What they really mean, and better English, would be for them to have asked, "Is that true?"