Personally, I think they are interchangeable in most of the cases. However we have to choose different words in some contexts. 普通话 refers to Mandarin or Standard Chinese, which is based on the particular Mandarin dialect spoken in Beijing. As you know 普通话 is most spoken language in mainland China, and then 广东话（Cantonese） . 中文 and 汉语 just refer to Chinese language. we might speak Chinese with different dialect, just like Mandarin VS Cantonese. But actually we share the same language in nature, which is 中文 or 汉语. As you said, 中文 is more of written Chinese language. In fact there're some other Chinese words for Chinese language. For example, Taiwanese would call Mandarin 国语 and you might hear people in Singapore call it 华语. I hope I'm not confusing you more than you are already.

中文=汉语，汉语分为普通话和方言，方言种类就很多了，有闽南话，粤语，四川话，上海话，北京话，江浙话，客家话等等，太多了。普通话是全国通行的语言、词汇、读音。

中文=汉语=Chinese, which do not only mean written Chinese, also can mean spoken Chinese. Mandarin=普通话, which means standard Chinese. Most Chinese people speak it. Even minority people, some of them can speak both his national language and Mandarin. As for Cantonese, it is a dialect, the same characters as Mandarin, but the different pronunciation. If you can speak a little Mandarin, sure you can say: "我会说一点汉语。" or“我会说一点中文。” （also, you can use character "讲" instead of "说"。） ps: Before I came to Italki I always thought Chinese language is just "Chinese". In my opinoin, the word "Mandarin" is bad for communicate (that's why you are confused now), Instead of "Mandarin", it should be "standard Chinese" . As for Cantonese, let me see..."cantonese Chinese"? haha, I feel it ok~

To my point of view, mandarin now is Chinese official language, which was originally created by Manchurian in the process of learning Chinese. Chinese consists of many regional dialects, like Cantonese still widely used by Cantonese and Hongkongers, Shanghai dialect, Manlam ngy, etc. And the pronunciation of these regional dialects are very different though their characters are the same.

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