Assume = suppose to be the case WITHOUT PROOF

• We can’t assume the suspects to be guilty.
• I’m assuming everyone here has a pen to write with.

Presume = suppose something is the case on the BASIS OF PROBABILITY.

• I presume they are not coming since they haven’t replied to the invitation.
• I presume he is Dr Rajiv Zachariah, the cardiologist because there’s a stethoscope hanging around his neck.