If you'll check the dictionary or thesaurus, you would somehow find both words the same, meaning SOMETHING TRUE. However, the usage would depend on the degree of certainty. Most of the time, when a person uses the word presumption, the tone of the sentence is usually more authoritative or confirmed. To presume is to say something with a feasible evidence or belief while assumption is more like a guess with little proof or none at all.

The man pointed out as the cookie thief was presumed innocent until proven guilty. They assumed he had taken the cookie even though there was no proof of it. In fact, the mouse, who nobody blamed, had actually scurried away with the cookie

Evhern gave a good answer. Presumption is more a deliberate stance taken with some thought -- as in, American court systems rely on the "presumption of innocence" That does not mean that the judge or jury thinks the person on trial is innocent, but that they should "pretend" the person is innocent, and wait to be convinced of guilt. Assumption is less often the result of deliberate thought. The person has often taken a wrong opinion about something, with no reason for doing so or basis in logic. Another slight difference is that, the person making a statement is more likely to think that he/she "presumed" while the victim of the falsehood will accuse them of assuming!

http://www.thefreedictionary.com/assumption http://www.thefreedictionary.com/presumption Just study the meanings carefully and you'll see the difference.