These words have related but distinguishable meanings. To assume is "to take for granted," "to infer without proof: "Mrs. Black assumed that her husband had paid the bill." To presume is "to believe something to be a fact," "to infer as true without actual proof to the contrary." When Stanley came upon another explorer in the jungle, he did not say "Dr. Livingstone, I assume" but "Dr. Livingstone, I presume?" because circumstances clearly indicated that the man he was meeting could be no one else. In ordinary conversation, however, the words may be used interchangeably.
Dictionary of problem words and expressions. Harry Shaw. 1975.