I always look at a sport as something where the two competitors/teams directly affect one another's "score". So basketball is a sport, for example, because there's defense involved, and the offense has to score in spite of the efforts of the other team.
I think of things like cheerleading, gymnastics, swimming, and the like, as competitions - not a "sport". There's competition involved, but it's not a direct competition in the same way as a sport would be.
It's purely semantics though, many "competitions" require just as much athletic talent and hard work as "sports" - it's just my way of classifying them.