Both expressions have the same use. For instance if your teacher just said "Your homework must be delivered by Monday" your teacher might say a few seconds later: "If you do not deliver it by Monday, I will deduct points from your grade." or "If you do not deliver it by then, I will deduct points from your grade." We use "by then" when the specified date has just been mentioned (or is implied) just to not sound repetitive. Also it can help you if you do not remember the date at the moment, and you do not want to spend time finding out, you can say "by then". Hope this helps!