Always Flyin, the definition of "non-stop" for this purpose is: does the customer make any stops between origin and destination? Two flights with the same flight number or two flights with different flight numbers, are both *not* non-stop.

The definition of a direct flight is one or more flights from the customer's origin to destination, all of which have the same flight number.

For example, if someone is flying DL from ATL to HSV, he/she can fly DL 289, a non-stop flight from ATL to HSV. That is also a direct flight, because it is "one or more flights" (namely one). You could also fly DL 289 from ATL to MLU via HSV. That is also a direct flight, but is not a non-stop, as the flight stops in HSV on the way to MLU.

As all non-stop flights meet the definition of "one or more flights with the same flight number", all non-stop flights are also direct flights. The set of non-stop flights is a subset of the set of direct flights.