Thing is, the technical physics definitions are really different from how they are used in normal language. If you go buy 2 pounds of bananas, you really are thinking of mass. You wouldn't expect them to cost any different on an elevator moving up or down, or something. So I think NASA is just trying to use the words they way people ordinarily do, in the non-technical sense. It's only a problem when you want to talk about the technical sense and people don't realize there is a difference.
It's a common problem in physics, makes teaching it hard. The chemists make up a bunch of weird vocabulary for their stuff, but physics tends to just reuse common words.