Why are the terms due-date and deadline synonyms?

The word "deadline" actually comes from the a term which originally meant a line around a prison that should a prisoner cross it, he could reasonably expect to be shot. A bit harsh and doesn't necessarily answer your question directly, but nonetheless it became a common phrase meaning the boundary of time you can't cross in order to complete your task. If your deadline is 12 noon, any time after that and the project fails because you're crossed the line laid out for your completion.