A "direct flight" is not the same as a "non-stop flight". If you're talking about a flight that goes from airport ABC to airport QRS, making no stops along the way, it's a non-stop flight from ABC to QRS.
A "direct flight" from ABC to QRS, is a flight that has one flight number... but that flight might make stops, and could even involve a change of planes. It's possible for flight ZX 1042 to be "direct from Podunk to Shanghai", and to have it be a puddle-jumper from Podunk to Chicago, have you change to a 757 there, go on to SFO to pick up more passengers, and then continue to Shanghai. As long as it's ZX 1042 all the way, that flight with two stops is "direct".
All non-stop flights are direct flights.
Not all direct flights are non-stop.
And, yes, even travel agents and airline booking personnel sometimes use these terms interchangably. If you're offered a direct flight, make sure to confirm whether it's "non-stop".
Barry