The file with a tilde is a temporary file saved by TurboTax in case the permanent file is unusable for some reason. You can just ignore it. You need to determine which of the other two files is the one you actually filed as your tax return.
When you transfer from a prior year, TurboTax populates a lot of the information that was on you prior year return so you don't have to enter it again. Things like names, addresses, and permanent information on forms like W-2s and 1099-Rs. This is very important for someone who has things like carryover depreciation or capital losses. It is less important for simple returns with not much more than a W-2. There is really no disadvantage to transferring unless one of the taxpayers has changed or you don't want to have to delete forms that transfer that you no longer need.
