The two creatures may be controlled by the same player.

If, by the time Rivals’ Duel resolves, an effect has caused the two target creatures to share a creature type, Rivals’ Duel doesn’t resolve for having no legal targets.

If either one of the creatures leaves the battlefield before Rivals’ Duel resolves, no damage is dealt to or by the remaining creature. If both creatures leave the battlefield before Rivals’ Duel resolves, the spell doesn’t resolve for having no legal targets.