Mandarin and Cantonese are regional dialects, Mandarin gained prominence because emperors from about the 1600s resided in Northern China and in Beijing which used a lot of Mandarin Chinese, thus it spread due to being a prestige language used by the royal family and their courtiers. Cantonese is prominent in certain areas of Southern China in the Guangdong and Guangxi provinces.
https://en.wikipedia.org/wiki/Mandarin_Chinese
https://en.wikipedia.org/wiki/Cantonese
Hong Kong and Taiwan uses Traditional Chinese, Mainland China and Singapore/Malaysian Chinese uses Simplified Chinese for their text.
https://en.wikipedia.org/wiki/Simplified_Chinese_characters
https://en.wikipedia.org/wiki/Traditional_Chinese_characters
I personally find fangyan as a better descriptor than dialect:
http://dictionary.pinpinchinese.com/definitions/s/%E6%96%B9%...