They're interchangeable as nouns. There is no difference. Drape can be used as a verb that means "to arrange (cloth, usually) loosely on or around"

Nowadays "curtains" and "drapes" are used interchangeably by the common folks, but people who work in the textile or theater industry may see a slight, insignificant difference. One being that "drape" comes from the word "drapery" which means thicker cloth or textile with certain class, elegance, and style, while "curtains" can be thinner(see through) and less elaborate. It is possible to have curtains and drapes on the same window.

I don't think there is one. However, if you are talking about the large cloth covering the stage of a theater, that is always referred to as the "Curtain" (at least in America, I've never heard otherwise) As 郭东兴 pointed out, drape can also be a verb.

'Drapes' is only used in North America (US/Canada). Elsewhere in the English-speaking world we say 'Curtains'.

The word 'drapes' isn't used at all in Australia (except as the third person conjugation of 'to drape'). We only say 'curtains'.