I have to disagree about "assume" only being used as a total guess. "Since I ordered it three weeks ago, I assumed that I would have it by now," would not be a total guess, but a logical expectation.
This is another pair where I think the only real difference is in the level of formality, and even that is slight and can depend on your tone of voice. Usually when I choose presume over assume, I'm being more formal, or else using it to convey my displeasure or skepticism, or both, because presume sounds a little bit stuffy to me. "I presume you know what you're doing with those explosives, right?" If I were seriously questioning their expertise, I'd use presume, but if I were teasing them, I'd probably use assume.
That said, the two are virtually interchangeable, so whichever one comes out of your mouth will be fine.
