Mostly I've seen 掃除 "souji" for "cleaning". Here recently I noticed an anime had a floor-sign for "closed for cleaning" using 清掃 "seisou". What's the difference?
Looking at the kanji didn't help any. Internet searches found uses of them near each other but no explanations (in English).
Dictionaries unfortunately don't help us much here. For 掃除 there is a nuance of sweeping or wiping something to make it clean, but 清掃's definition isn't really different in essence and is defined in terms of 掃除 anyway. There might be a nuance with 清掃 of cleaning something to completion, but it's tricky. So what does the internet have to say?
Some answers around the net seem to agree that 清掃 has a much more thorough image of cleaning something down to using chemicals and whatnot to do the job. Colloquially this may be the case.
I think a more logical answer, however, as discussed here, is that 掃除 is just a simple act of cleaning with no special scope or connotations to it while 清掃 tends to be more official or large scale big-C "Cleaning." This would include government agencies or other vocations that involve cleaning to some extent, for example [清掃従業員]{せいそうじゅうぎょういん} or [清掃法]{せいそうほう} or [清掃局]{せいそうきょく} or [清掃用具]{せいそうようぐ}, just to name a few. None of these work with 掃除, which really connects only to things like [掃除機]{そうじき} or [掃除当番]{そうじとうばん}.
So when you clean your room, you're doing 掃除. When you're cleaning the city, you're doing 清掃. Or something like that, anyway. Ultimately it's an issue of scale or profession.
You can peruse the following alc links to see more usage examples:
http://eow.alc.co.jp/search?q=%E6%B8%85%E6%8E%83&ref=sa
http://eow.alc.co.jp/search?q=%E6%8E%83%E9%99%A4
Given the many, varied examples of how 清掃 is used, it seems to be just a general term for "cleaning" that can be used in just about any context, from "teeth cleaning" to "street cleaning". 掃除, on the other hands, does seem to be restricted in its use to situations where "sweeping" or "wiping" or the like are involved. You could say, couldn't you, "浴槽を清掃する", but would "浴槽を掃除する" be appropriate?
