The first two are adjectives, and the third is a noun, and they are used differently. Sporty is typically used to describe clothes, and has nothing to do, per se, with sports: That's a sporty outfit. Sporting is typically used to describe conduct in some kind of contest (not necessarily in sports) that is gentlemanly: In a close match against a good opponent, he gave his opponent a disputed point, a very sporting gesture on his part.
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