To me, both of them are similar, with a slight preference to alcohol for the first one, and non-alcoholic drinks for the second one. I would feel happy answering either question with either an alcoholic or non-alcoholic drink. 'drink' certainly isn't only wine. It could be any alcohol. Are you perhaps confusing the meaning of 酒? However, we tend not to use 'beverage' here much, so my usage may be different to other parts of the world.

What's your favorite drink? (This would typically be used for hard alcoholic drinks, not wine or beer) What's your favorite thing to drink? (Open ended question. Milk, whiskey, wine, coffee, Red Bull, water from a spring on my grandfather's land, etc. i.e. most things are something you can drink, but not often called "drinks") "Beverage" is a more official word and tends to make me think of a category. "Nestlé is the world's largest food and beverage company" My answer to "What's your favorite beverage?" would be "What do you mean by beverage?" As far as Bramwell's usage of beverage, I would use "hot beverage" to mean tea, coffee, cocoa.

To my British mind, beverage has a narrower meaning than drink. Beverages are hot drinks, like tea or coffee, or alcoholic drinks. Soft Drinks like squashes, juices or fizzy drinks I would not consider to be beverages, neither is water a beverage. All beverages are drinks, but not all drinks are beverages. This is how I have always used the words

I think beverage and drink have exactly the same meaning and can refer to anything listed above, including alcohol and coffee. Except for water: it is always a drink, not a beverage.

I like to drink red wine