There is no difference between the mobile app and TurboTax Online, The iPhone/Android app is TurboTax Online, but formatted so that it's easier to use on a phone or tablet.

Normally, when you use TurboTax Online, you would pay per return. The Deluxe package they sell at Costco allows you to file 8 deluxe returns at a discounted price. If one (or more) of your 8 returns needs to be upgraded, then for that return you would be credited the price of 1 Deluxe return, and you would only have to pay the difference.