Expedia.com used to have an option "direct flights only". If you check that box, you would get both non-stop and multiple-stop direct flights. They've since changed it to be "non-stop flights only", probably due to customer complaints about the direct flight "scam". The definition of a direct flight is one or more, not two or more, flights with the same flight number.

Re passenger's itinerary between two cities vs the airline's service between two cities -- it's the same thing. If you want to fly between LGA and DFW on UA, not only is there no non-stop service, there is no direct service (there used to be a direct flight through IAD).