中文 mainly means written language, whereas 汉语 tends to refer to the Chinese language you speak. However, most Chinese people don't differentiate the two words nowadays, so you're free to choose either of them whenever it comes to spoken language or written language.

The biggest difference is that 汉語 is referred to the language of the Han Chinese. This is used by countries that uses the Chinese script such as Koreans, Japanese etc to differentiate their own language. 中文 is a newly coined word made up after the fall of the last imperial Dynasty to encompass all languages spoken/written in China (it means the languages of 中國. In the old days, there's no such thing as China. It is called 大唐, 大宋, 大清 after the ruling dynasty). Since Han Chinese is overwhelming the majority, the west mistook the term and referred it to the language of the Han Chinese.

中文和汉语有的时候是一个意思，有的时候是有却别的，如“他教中文”，意思是他是个大学的老师，教中国人学中文，再比如，“他教汉语”，意思是他教外国人学习汉语或中文。

Generally speaking, 中文 includes 汉语. China is a multi-ethnic country, embracing Han，Manchu, Mongolian, Korean and many other ethnic groups, in which 汉语 is just one ethnic goup's language and doesn't includes other ethnic languages. Due to the large population of Han people, 汉语 naturally became the main language of China and the official language for generations.汉语 usually refers to spoken and written language, but 中文 includes more, such as reading and writing.

originally 中文 = written 汉语 = oral but actually -- no difference at all