A 'direct flight' is generally the same plane and flight number but can include intermediate stops. You still see them on occasion in many different places, particularly if logistics require a refueling stop (example- common for really long haul flights out of higher elevation airports like Mexico City to have to refuel because of physics reasons) and the stop may or may not be treated as a valid place to get on/off the plane.

Many people confuse 'direct flight' with 'non-stop' which is the specific language you need for a flight that is actually non-stop.