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Mathematically, no, there is no difference.
However, if you're playing a card game that requires deck manipulation, you will of course want to generate the whole deck at once, because you might need to perform actions like placing a card from your hand on the bottom of the deck. You can't do that if the rest of the deck doesn't exist yet.
If you're generating cards at draw time, it can get expensive to check to see if a card has been generated yet, because you'll have to check the table, everyone's hand, and the discard pile. Or maintain a separate list of all cards generated so far, but at that point you might as well have just generated a whole deck in the first place.
Ah! This is something that I hadn't directly considered. Interesting point, and it could be a serious concern for some games.
Thanks!