Assume and presume both mean to believe something before it happens, but when you assume you're not really sure. If someone bangs on your door in the middle of the night, you might assume (and hope!) it's your crazy neighbor. If your neighbor knocks on your door every night at 6:30, at 6:29 you can presume she's coming over in a minute.

To assume is to suppose or believe something without any proof. It also means to take over, usually responsibilities and duties, such as with a job, or to take on a look or attitude:

First, based on your question, we'll assume you're a recent college graduate. (USA Today)

Receiving no reply, three days later he sent a second missive, in which he assumed that his first letter had gone astray. (Elizabeth S. Kite)

"I won't have him," said Sir Henry at once, his eyes assuming their most prawnlike expression. (Mary Cholmondeley)

Presume is from the Latin pre, "before" and sumere, "to take," like taking something for granted. It means to be sure of something before it happened. When you presume, you suppose something without proof, based on probability:

"I presume you are just as cold as we are, so let us complete this transaction as quickly as possible." (The Thief Lord)

When I just stood there, dumbly watching her, she lost her smile and said, "I presume you’ve heard I’m sick." (October Sky)

People don't love it when you assume because you're basically making a guess. When you assumed it was your neighbor knocking on your door and you told her to go away, you found out later it was your mom! There's no funny phase about presume, because you're usually right.