Are you using the zip version or the installer?

64 bit installer

it sounds like you might have 2 versions of the game installed, the demo and the full version.

I think that's true however both versions of the game show the same list of saved games. Last night I played and when I saved, I saw ...

I had played the demo and made several saves. Yesterday I bought Factorio, downloaded it, played for a while and then saved the game. When I came back today, I can only find the saves from the demo games and everything from last night seems to have completely disappeared. Last night when I was ...