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 (?)