They are synonyms. :) Assume and presume both mean to believe something before it happens. (No Proof) Ex: When your friend is late for work, you assume their alarm clock didn't go off. Ex: When your friend is is always late for work, you presume their just sleeping in, like normal.

Many times, 'presume' and 'assume' mean the same thing - to believe something without proof. "I assume/presume that he will teach his class this semester using the same outline as last semester" However, 'presume' has another meaning, different from 'assume'. It can also mean to behave in an overconfident manner. "Don't presume to tell me what to do! You have no authority here!"