While I studied aviation, I got confused by these two words. Can anybody explain whether they're the same or not, and if not, what is the difference?
For the simple case, yes. The threshold will be the end of the runway. The AIM has a graphic showing standard markings past the a normal threshold.
However, the airport operator may decide that aircraft should not land at the end of the runway. This may be temporary (perhaps for construction), or permanently (for obstacle clearance or noise abatement). In such cases the threshold is moved and marked away from the end of the runway. When permanent, this is called a displaced threshold and will reduce the landing distance available (LDA) to less than the length of the paved runway.