1. Part of it is because you just applied. Applying always lowers your score. There are no exceptions. Applying only once shouldn't lower it 58 points, so there's probably something else as well, but applying is definitely one of the reasons, even if it's not the only one.
2. No one can have only one score. Anyone with a credit score has more than one, and the one that the application shows isn't likely to be the same one as you see when you check your score. It's like comparing Fahrenheit and Celsius temperatures. Both scores may have gone up. For example, it could be that the score that was 710 when you checked is 720 now and the score that is 648 now was 638 last year. You can't tell whether you score has gone up or down by comparing scores from different places. That only tells you that the score you checked is higher than the score that the application shows, which doesn't mean anything about whether the scores have gone up or down.