We download entire websites - not just one page. For every domain, we download up to 20,000 URLs/pages.
If you can browse to a page, by starting from the front page from a certain date, then we download that page. Our software works like a human user who clicks on all links on the front page. Then it will visit those links and again click on all the links it can find on those pages. It will continue like this until it found all pages.
For every URL, we download only 1 version. So if domain.com/page1/ was archived by archive.org on multiple dates, then we only scrape 1 date.
This date is usually close to the date that you picked for the front page. If you picked a front page with a date from 2016, and our scraper finds an inner page with 2 dates, then we recover the page that is closest to 2016. For example, if you choose https://web.archive.org/web/20160315050823/www.example.com as the front page, and we see that example.com/page1 was archived in 2015 and 2018, then we recover the 2015 version.
For more information, see this blog post: Improved backend now also recovers pages without internal link path