Thanks, after reading your responses and scrolling farther up up on the thread, it looks like someone had a similar question before that may have gotten to the crux of what I wasn’t understanding. In the scale diagram I saw all of the string names listed along the top and I thought they were just there for reference. I now see that they are actually blacked out with white font which I now think indicates they should be played. If it was a scale in which an open string should not be played, I now believe they omit that string name along the top as the did in the screenshot of this unrelated scale included first below. I included the scale I originally saw below that. Is that correct?
Ah, I see the confusion! You’re exactly correct - if the open string were not to be played, it would not be named. Sorry I didn’t see that sooner! As an aside, I think the C major open scale diagram could be improved by making the marker for C on string 2 red, as it is a root note.