'Aufräumen' is more like 'to tidy' while 'sauber machen' is like 'to clean up'.

Example: Imagine your kitchen cupboard.
Scene1: The plates, cups, etc are perfectly hygienic and clean, but not sorted. Big and small plates are mixed, the cups and glasses too, everything is in a chaos. You might look at it, shake your head and hear yourself say: 'Das muss ich aufräumen!' ('I have to tidy that'.)
Scene2: The plates, cups etc are perfectly sorted, but they are dirty. Now you'd say: 'Das muss ich sauber machen.' ('I have to clean it up'.)