There is a big difference. It all comes down to the fact that for financial derivatives, there's an underlying asset that can be bought and sold, allowing for hedging and arbitrage, which is not possible in gambling or betting.
Let's assume a casino offered a "fantasy SPX option" game. A computer randomly generates a fantasy S&P 500 index that changes by the minute, just like the real S&P 500, a random walk with the same (positive) expected annual return and the same volatility as the real S&P 500. The graphs of the real and the fantasy index would of course diverge but would look roughly similar. Now the casino allows you to buy or sell call options on their fantasy SPX. These are cash-settled options and the market would work just like the one for real SPX options.
You'd see that the prices of real SPX call options and fantasy SPX call options would differ dramatically. The reason is that you cannot buy a bundle of stocks that replicates the fantasy index, but you can do so for the real SPX. This means that you cannot hedge, you cannot arbitrage, and Black-Scholes pricing would not apply to the fantasy market.
If you buy or sell a fantasy call option in the casino, your expected return will be zero (or slightly negative if the casino takes a cut). If it were positive, say, the sellers would raise their price until the expected return becomes zero. Unless they are dumb.
If you buy a real SPX call option, your expected return is positive (assuming that the true expected annual return of the S&P 500 is large enough and the fees don't kill you). The sellers cannot simply raise the price of the option, because then arbitrageurs would show up; by cunningly borrowing the right amount of money and buying the right amount of the S&P500 stock bundle, they could offer to sell a cheaper call option and extract a risk-free profit from the buyers, pushing the other sellers out of the market. Why are the sellers selling options if the expected return of doing so is negative? They are essentially buying insurance. Buying insurance always has a negative expected value.