These terms come from wood and metal working terms. An edge that is cut at a 45 angle is said to be chamfered. A corner that is smoothed until it is rounded is filleted.
As an example: Let's say that you are making table legs out of wood. Perfectly square table legs might look cheaply finished, so a common detail is to cut the sharp edges of the legs at a 45 angle. The name of that cut would be a chamfer.
If you were making a part that had a sharp edge, you might fillet the edge so that is not sharp.