The file with the tilde ~ means it is a temporary file that for some reason did not disappear on its own. The true tax file from last year that you want to transfer should not have the tilde. Do not transfer from the ~ tilde file.
After you confirm that the transfer from the true data file is successful and all the data is correct, at some point you could delete the file with the tilde. It could be a temporary file from the late stage of your 2016 preparation, or it could be temporary file from an earlier stage of your preparation. It can serve as a sort of backup during return preparation if someone were to lose their data file somehow, but it might not be the exact version of what they had just been working on. I suppose comparing the file date to the date of the actual data file might offer a clue.
But I wouldn't count on a tilde file for backup. And it's not always generated in any predictable fashion, and it could disappear on its own.
You should be making your own data file backup frequently during preparation and not counting on a tilde file. I save a copy of my *.tax2017 data file after each session that I work on my return. I copy the data file to a flash drive each time--just in case. You can also save to other types of external media, external drive, etc.
