Someone with the preference appreciation finds it important to be appreciated by others. This motivates the person to keep going on a task for example. If this person doesn’t get any appreciation, they can lose the trust and respect in themselves. They could also lose their motivation to help someone who is not showing them appreciation.
Someone with the preference achievement finds it important to succeed and to be able to show this to others. The motivation to get results becomes even stronger, when someone solves problems and delivers purposeful achievements. These people also like to mention to others certain achievements that they are proud of for example, (I made this!).