I have found that zh-CN and zh-CHS both of them can be used as language code, but why microsoft only tells me only zh-CHS can be used: http://msdn.microsoft.com/en-us/library/hh456380.aspx.
Would it make any difference?
There is quite a lot of confusion with these codes, because they all look similar but may mean different things.
If you take a peak in CultureInfo docs, you'll see that zh-CHS refers to a "Chinese Simplified" culture, and zh-CN is a more specific culture code which means "Chinese Simplified, People's Republic of China" (e.g. same language as used in a specific country, a child culture to zh-CHS parent).
I suppose it does not make sense to use country-specific culture code in the context of Bing translator (e.g. both cultures use the same language, but zh-CN is more specific and lets you distinguich Simplified Chinese in PRC vs Simplified Chinese in Singapore, zh-SG).