Online vs. Paper- the only two answers that make sense to me are Online or Makes no difference. If the drawing is completely fair then it makes no difference where the tickets come from. But I sometimes suspect there's an imbalance for advertising reasons... for example, lottery subscriptions just became a thing and both Powerball and MegaMillions already had a solo jackpot winner with a subscription. That's a huge coincidence. Great ad though. Online sales of draw games is new too, and having a winner who bought online is a fantastic ad.
We also tend to see jackpots roll over too many times even when hundreds of millions of tickets are sold (enough that the expected number of winners is >1, as happened on Tuesday) over and over again... for example, inflation being what it is now I am expecting this jackpot to roll over with no winners so that they can declare the "largest jackpot ever" next week. It's statistically unlikely.
Looks like I'm the only one who voted so far.