Presume and assume can both mean ‘suppose’ and are often used as if they are interchangeable. However, there is a difference:

• Presume: to suppose something is the case on the basis of probability.
• Assume: to suppose something is the case without proof.

Usage of assume that is more common than presume that, so assume may feel more natural to use in conversation.

Both assume and presume can also mean ‘to take on oneself’. The usages are usually as follows:

• Assume: to take on a role.
• Presume: to take on an attitude.