svartvit just focuses on them having no other colors. If you say either vita och svarta or svarta och vita, it is likely that whichever color you mention first dominates. It is quite possible that you are talking about multiple curtains, of which some are white and some black, though it does not have to be that way.
It's often used that way, and of similar things, like en svartvit syn på världen 'a black and white view of the world', but I wouldn't say it's exclusively for that. More like it's closer to monochrome in meaning.
Btw there's a bird called svartvit flugsnappare, called European pied flycatcher in English, where svartvit actually means svart och vit. – You're right black and white movies can only be called svartvita though, I just don't think it explains the whole difference. It's more like, once you have two expressions for something, there will usually be some distribution.