There is no real difference between the two rewards.
As representatives of their Master, who himself was sent by One greater than himself, the apostles would be perceived differently by different people. More important than how the apostles were perceived was whether or not they were received.
Whether their audiences perceived them as prophets and received them as such, they would be rewarded by the apostles' Master for believing in him, the subject of their message. (By the way, Jesus himself was a prophet who when he came on the scene was his Father's mouthpiece, declaring the kingdom of God/heaven was at hand and telling people to repent.)
If audiences perceived the apostles as righteous men, they too would be rewarded by the apostles' Master for believing in him. Evidently, the apostles' righteousness exceeded the righteousness of the scribes and the Pharisees because they believed in Jesus, whereas the righteousness of the religious insiders of Jesus's day was markedly inferior because they did not believe in or receive Jesus as their Messiah. They were believers in God, and they were scrupulous followers of the letter of the law, but in their hearts they were not truly righteous.
In conclusion, whether audiences perceived the apostles and their message as coming from prophets of God or as righteous emissaries of God, they would be rewarded for their faith. The greatest reward for their faith, belief,and repentance was being accepted by the Messiah who sent his disciples as his representatives and messengers.