Okay, first of all, great game. Second, I wanted to update to the latest version but I don't think that there is an update function. Am I blind or am I going to have to download the latest then move my save
If you're expecting some sort of system that updates the game for you, sorry, there never has been.
You can download the new file and delete the old if you want.
As listed in the download section above, you can also use a patch to apply just the latest update alone to the last version, if that's what you have.
As for saves, they are stored elsewhere on PC and will always be safe. On mobile, yes, move them from the old file to the new one.