vocabulary - When is 酒【さけ】used to mean 日本酒【にほんしゅ】?

The fermented rice alcohol called "sake" in English is usually referred to as 日本酒【にほんしゅ】 in Japanese, while 酒【さけ】 merely means "alcohol" in general.

Yet, all dictionaries list both "alcohol" and "fermented rice alcohol/sake/nihonshu" as translations for the word 酒.

Lately, I have noticed 酒 used a few times in movies to mean "nihonshu" specifically (e.g. with one character ordering a beer, and another ordering "sake").

I imagine the use of 酒 for "sake" was the standard in ancient times (and only evolved after the introduction of other popular alcoholic beverages), but can anybody tell me if there is any modern context where it is still commonly used? In such a case, would it be more or less formal?

Edit: Yuji's answer below also made me realise that the use of the polite form (お酒) might play a role in differentiating the two senses (?)

Answer

I think this is somewhat equivalent to ご飯、which was also confusing enough to warrant some questions (admittedly, non of them about the dual meaning of the word, but the issue became prominent in both threads).

In essence, you can say that ご飯 generally means a meal, but can also have the more specific meaning of cooked rice. This more specific meaning also serves as a default meaning of sorts: depending on the context, you may assume ご飯 specifically refers to cooked rice.

In the same way, (お)酒 may mean alcoholic beverages in general (equivalent to the English 'booze', except that the latter is very informal) or 日本酒 as its default more specific meaning.

This is not an uncommon phenomenon at all. A few decades ago (and to some degree, it's still true today), 'tea' generally meant any beverage made by extracting the flavor of tea leaves, but the default meaning was black tea. If you wanted a cup of green tea or oolong tea, you'd usually have to explicitly ask for it - otherwise you'd just get black tea (and with an atrocious heapful of sugar at that :)). In Japan, on the other hand, the default meaning of (お)茶 was (and probably still is) 緑茶, that is green tea.

This is all very culturally dependent, and rather easy to explain, though there are some cases where such a 'default meaning' doesn't have much to do with culture. I can't think of English or Japanese examples for such cases, unfortunately. :(