Substantively "中文" and "汉语" refer to the same language as far as language learners like you are concerned. For those who wish to delve deeper, it is essentially a matter of nomenclature and political assertion. The phrases "汉语" and "普通话" became official nomenclature in the People's Republic of China in the 1950s. Together with simplified characters they became emblems of a particular regime, while at the same time in the world there has been another system using terms such as "国语" and traditional characters for 中文. All this took place against the background of a national history of thousands of years which included fragmentation and "foreign" domination by the Mongols and the Manchus. It became a matter of political struggle at the United Nations as well. There are certain linguistic and social arguments for the use of these terms, politics apart. You have unwittingly, or intentionally (who knows?!), asked a political question. There is nothing wrong with that except that there is not enough space here to give a full answer. You can search the internet for the historical and political background of this interesting subject as well as the debate that is still going on now around the world.

Basically, 中文 and 汉语 are the same thing. They are interchangeable. Cantonese is one of the dialects. People in Hongkong and Guangdong Province speak Cantonese. People in other cities speak different dialects. All dialects are based on 中文 or 汉语, they just have different pronunciation or tone, in some cases, one dialect includes some unique words that people with different dialect don't use, but those words account for very small part of all Chinese characters. English speaking countries may not have dialect, it's just that people in different places have different accent. However, in China, you cannot just use "accent" to describe the difference in pronunciation because the difference is too huge. Some dialects sounds like a totally different language. For me, Cantonese sounds like a foreign language to me.

汉语是指有几千年来汉民族使用的语言，”普通话“，这个名词只有几十年的历史，二者是不是一样就知道了。”普通话“是个奇怪的术语，”普通“对应的是”不普通“或”特殊“，而事实上，它对应的应该是“方言”，而和“方言”对应的应该是“官话”或“国语”。古代用“官话”这个词，好象民国时才用“国语”。 “中文”：”中国的语言文字”，严格的说，“讲中文”是不准确的。但很多人这样用，大家也就接受了。讲究一点的话，可以说“用中文”，“使用中文”，“译成中文”，讲汉语、说汉语，讲中国话等等。

you can 讲中文， which shows 中文 means not just written Chinese

汉语 = 普通话 = oral Chinese, 中文 = written Chinese