Presume and Assume. Although they're used interchangeably now, to presume originally meant to assert that something is true without complete evidence; to decide something without absolute certainty. (Since absolute certainty is impossible, you could say that we presume everything, including the physical condition of the world.) To assume, on the other hand, meant to acknowledge that not all evidence was in, but to act as though something were true.

Presume is used when we take something for granted or take advantage of something or someone. Assume is used when we undertake something in an arrogant way. Can also mean take for granted. 'I assumed that I would be the next President of the United States'.