I don't think there's a precise scientific definition of "bug"

Yes and no. There's a group called "true bugs" (https://en.wikipedia.org/wiki/Hemiptera as linked above). "Bug" in the common sense doesn't have a precise definition (small arthropod that may or may not be a pest to humans is about as precise as I feel I can get), but there _is_ a scientific definition of "true bug".

So moths are not bugs because they're "true bugs"? How does it make sense?

Apparently they're not "true bugs", the comment you replied to isn't claiming that they are.

This is the kind of response I appreciate. Thank you!