I think the difference is that the date search is for finding stuff that was originally posted / crawled in that date range. (I believe) the original comment was regarding searching some HTML, for example, as it was at that date.
That is to say: if you had a page that changed over time, you would be able to search for that page as it existed in a particular date range, not just searching for a page that was posted / first crawled in that range.
That is to say: if you had a page that changed over time, you would be able to search for that page as it existed in a particular date range, not just searching for a page that was posted / first crawled in that range.