Difficult to say without knowing the exact context. I disagree that these mean the same thing.

Sarah is correct. I would give her a thumbs up if she had posted her answer under answers instead of comments. (This new italki system is confusing because the comment box is always visible.)

Thanks Sarah !!!

They both mean essentially the same thing, though "respond" is slightly more formal. I would probably use "She didn't respond" and "How should you respond?" because "respond" is more general, whereas reply would be used just in terms of replying to specific outreach (e.g. email, text). If speaking at all or writing informally, I would always shorten "did not" to "didn't."