Why is gambling legal in the UK and other European countries but not in the US?

The United States is governed by federal law, which does not prohibit gambling. But each state has its own laws that supplement federal law. Almost all states prohibit gambling for US citizens except Nevada, which explains the presence of casinos in Las Vegas. There are states that only accept online sports betting and those that accept online casinos and others that accept both. You should know that online gambling is legal in the United States, but it is the States themselves that choose to authorize this activity and under what conditions.

Each land had its own rules, so there will always be a different law in each country.

here in the United States the legality of gambling falls to the state. you can look at Oklahoma where they have Indian casinos, and online gambling or you can look at a place like Las Vegas, which has everything you can imagine and then you look at my Home state of Texas. All have a horse racing. and there's nothing wrong with any of that either direction. It's just up to the people in their state on how they want to live and conduct themselves.