Apparently, both of these mean Chinese, and the Chinese language. I gather that 中文 is maybe more like "written Chinese," and 汉语 is "spoken Chinese." Is this correct?
I've often looked at BBC zhongwen, so it makes sense that that's "written". If a movie was in Chinese, would you say 汉语 for that?
Can you give more examples of each, particularly when you could only use one or the other? Are there any examples in which you could potentially use either, with a slightly different meaning?