Dang, I was like..this is a funny question that i will say a joke, but then i actually thought about it for a sec and look at this.
The difference between the lottery and the Hunger Games is one is about winning lots of money and being famous for a day or two, and the other is about getting picked to kill someone, and also endangering yourself.
Get this. You can win the lottery by chance just like hunger games. Once you win the lottery, it has been seen multiple times before, people will usually blow it all, and become super poor, maybe becoming addicted to drugs and whatnot. With hunger games, (as we've seen before) you get one chance to make it big with your winnings otherwise you meet your demise.
So all-in-all the Lottery isn't very different from Hunger Games at all. Hope this helps :)