My alert shows a large number of responses but when I "Download Survey Responses", the results are less than the number of alert responses.
The confusion here is that just because someone took your alert, that doesn't mean that they answered your survey questions. Alert respondents will only show up in the survey response report if they answered the survey questions added in the "Include Questions" step when configuring the alert. If you want every constituent who takes the alert to show up in the survey report, you will have to ensure that at least one of those questions is required so that everyone answers at least one question. Note also that if you add questions to a questionless alert after some constituents have already taken the alert, those constituents will never show up in the report.
If you need all of the constituents that took the alert and their survey responses, you will have to run and download two separate reports. There is no single report that contains both the survey responses for the alert and the alert responses at this time.