As many of you know, since you are advanced technical SEOs, /page and /page.html technically are different URLs and different pages. But often, web servers are configured to make the page the same, so if you go to /page or /page.html, either you get redirected to one or the other OR you see the same content on both pages.
But since they are technically different pages, if /page and /page.html have completely different content – then Google technically can rank those pages separately for different keywords.
Gary Illyes from Google confirmed this on Twitter recently:
Sure, we can index both of those, if they have substantially different content
— Gary “é¯¨ç” Illyes (@methode) June 26, 2017
As long as the content is different enough, sure – Google can index and rank both.
But it is probably recommended you don’t play those games and keep things as simple and consistent as possible. Use a different URL for different content and redirect one to the other in this example above.
Forum discussion at Twitter.