They send it the same time. The savings is however long the post office was taking to deliver the checks. You get it whichever day EDD was mailing the checks.
If you live close enough to EDD so that the mail takes one day in each direction, then they were getting the claim forms on Tuesday, taking two days to process them, and sending the checks Thursday, so you will get the money Thursday, one day sooner.
If you live far enough so that the mail takes two days in each direction, then they were getting the claim forms Wednesday and sending the checks the same day, so you will get the money Wednesday, two days sooner.
If the mail takes two days in one direction and one day in the other direction, then it will be either one or two days sooner.