- The Payout: Rarely would you ever see your money x1000000000 in a casino, but in lottery, that's the entire premise. You put in as low as a dollar on the line, and you have a chance to claim a stake at huge amounts of money.
- The Luck: Most casino/gambles involve unfair yet doable odds. 40/60 house edges being one of the most common odd disparities in this market. In the world of lotteries however, you get as much as 0.00000001% chance at winning, sometimes even less.
Lottery is just another gambling game. The ticket is cheap, the prize is huge, just like at traditional casino games where the less winning chances you have, the higher it's going to be the multiplier, while when playing with high winning chances, the prize decreases considerably. The odds work in similar manner in lottery and other gambling games.
- The Replayability factor: Casinos set a premise where even if you win today, you'd always get the chance to win again tomorrow, lotteries do not have that liberty, with most people who won the lottery knowing fully-well that they wouldn't have the chance to win again in the future.
Also, just because you won once in lottery, it doesn't mean you can't win anymore in your life. The chances are always there, just like at other gambling games. What happens is that chances are too low, although they don't decrease from the first win to a potential second win.
- Access: Casinos are age restricted and are mostly region-based. A casino couldn't cater to anyone beyond their area, but lotteries like powerball are played on a national scale, sometimes even international.
And casinos are so accessible or even more accessible than lotteries. You can play casino games anywhere at anytime, since you have internet connection. You can do this from wild countryside regions, but you can't play at the national lottery from there, as it demands you taking a vehicle and going into the nearest city's lottery to place a bet. Casinos are digital, while national lotteries are physical.
But I agree with you that lotteries aren't age restricted, because I've already seen underage people purchasing tickets and playing in the absence of their parents. However, that was in physical shops. At online platforms which ha lottery included, underage gamblers won't be allowed, anyway.