Hi, the word alcohol covers drinks like vodka, champagne, brandy, whisky, wine, port, liqueurs etc. If you want to ask for an alcoholic drink you could say, "I'd like a white wine/champagne/ whisky thanks". Booze is the slang word for alcohol.

Booze is the informal form for alcohol that you drink. You can use booze in a funny, joking way. The common word to use is alcohol. People know from the situation that you mean alcoholic drink and not "rubbing alcohol" or other type of alcohol. "That restaurant doesn't serve alcohol." "Teenagers are not allowed to buy alcohol."

Booze, being slang, is generally associated with cheap liquor, unless said jokingly. You can also say "(he is) on the booze" as a slang, meaning someone is drinking (perhaps habitually).