I always thought about odds that it's all about how much money the bettor will win and the probability that it will happen so I was surprised that there is a debate if odds and chances are the same.
You just said that odds are the probability of that thing happening.
Now if one bookie has PSG at 2.15 and one Bookie has PSG at 2.3 against Bayern next week, how do you calculate the probability? Because by definition, you can have two probabilities of an event happening

I agree with you that in gambling, the concept of chance is not the same as the concept of odds on a sporting event. However, in my opinion, these two concepts are interconnected. That is, there is no identity, but there is a correlation... 😌
Correlation doesn't imply causation!
Live bets on events like elections, Oscars and other stuff are the perfect example. Trump had the same "chances" before the polls closed and one hour after, his ods on winning and going down after the event happened and it was immutable, is proof of them not being connected to the probability of that happening.