You can gamble on the stock exchange, just like you can "non-gamblingly" hedge certain risks by buying/selling certain financial products such as event futures. (Many insurance policies are structurally just that and are used for very boring non-gambling purposes!)

I don't think you'll find a simple/useful answer by slicing the problem on that axis.

At least when I put money in the stock market, I own a piece of the companies I'm invested in. I get some small amount of voting rights.

You don't get anything outside of winnings or losses from your bets on a "prediction market".

Sure, but most retail shareholders don’t make use of that right, and it’s severely diluted compared to preferred shares to boot.

That’s what I mean: Many things can be used in very different ways. These incentives usually matter more than the underlying things in finance.