There is no difference ,the verb 'suffer' means the same . 'From' is a preposition added to compliment a sentence and acts as a conjunction to indicate the reason.

Thank you all so much

They mean the same thing, but "suffer from" is how you explain why you are suffering. You wouldn't normally say, "He is suffering because/with malaria," but you would say, "He is suffering from malaria." There are, of course, always exceptions (eg. I'm suffering because he broke my heart,), but generally, suffer from is used to explain the reason.