JS:

I agree with your first paragraph.

However, I disagree with the remainder of your post. A non-stop flight is not also a direct flight. A direct flight has two or more legs--not one.

The other confusing factor is that you can speak of a particular passenger's itinerary as direct or non-stop, or you can speak of an airline's service between two cities (e.g., UA offers direct service between XXX and XXX.)