'Rewards' are items your players can redeem using the points they have accumulated. Rewards are added at Project level and are found in the Rewards Store.
Rewards motivate your players to earn more points so that they can redeem the goodies they want.
'Achievements' are badges that players can earn and keep. Achievements are added at Topic level. They usually come in the form of badges.
You can award your players these achievements when they've completed a certain number of challenges, completed an entire module, accumulated a certain number of points...
Achievements will motivate your players to continue playing the game. In the example below, there is a total of five achievements in the topic. Players will be motivated to unlock all five and, hence, will continue playing.
In a nutshell:
Rewards are physical items players can redeem using points accumulated. Achievements are virtual awards given to players throughout the game.