Gambling encompasses a broader range of behaviors that also include risking money with unknown outcomes, but betting is a type of gambling since, as I've mentioned, it involves anticipating specific outcomes.
For me it would be just like this:
Gambling is when you're putting money on the line with the hopes of winning more money or some other prize. Think of stuff like playing cards, slots, poker, or roulette at any casino could be online or in-house. It's all about taking a risk and hoping luck is on your side.
While betting is a bit more of specific. This happens when you are wagering money on the outcome of something. This could be a sports game, a horse race, or even things like who's gonna win an election or the Paul vs Tyson. You're basically saying, "I think this is gonna happen, and I'm willing to put my money where my finger pointing is."
So, gambling is the bigger umbrella term that covers all sorts of games of chance and probabilities, while betting is more about predicting outcomes and putting your money down accordingly.