What is the difference between an Inference and a Presumption?

Proof of a fact can lead to the presumption that a related alleged fact is true. That is in itself an inference. You infer based on a presumption.

Legal jargon.

Speaking as an attorney, my opinion is that an inference is a conclusion, tentative or otherwise, which may be drawn from other facts while a presumption is legal rule which says that the conclusion must be drawn unless proved otherwise.

For example, suppose a person is exiting a retail store and an exit alarm sounds. The person is stopped by store loss prevention and it is discovered that she has an item in her purse that is the same type of thing the store sells and it has a security tag on it that has not been deactivated by a cash register scanner. It is a permissible, commons sense inference that the person shoplifted the item. However, anyone examining the facts is not required to draw that inference. There may be other explanations for the event, not the least of which is that the person bought the item legitimately somewhere else and the cashier did not scan it properly.

Here is a legal presumption. To evict a tenant it is necessary to give them a notice. Suppose that a landlord puts on uncontested evidence that on such and such a day she mailed a notice of termination to the tenant by US mail to the tenant’s address. There is then a legal presumption that the notice was received by the tenant. The tenant may deny it and if the tenant’s evidence is strong enough the tenant can overcome thte presumption. However, unless the tenant dooes put on opposing evidence the conclusion compelled by the presumption stands.

Hope that helps.