The Chinese language is written in only two forms today. One is Traditional and the other is Simplified. Using "Chinese" is ambiguous.
Also, what you call "Chinese Classic" is commonly called Chinese Traditional. Calling it "Chinese Classic" could be referring to Classical Chinese written centuries ago, which is no longer used.
Reply: In our site, Chinese (zh-cn) means Chinese Simplified for mainland China, Taiwanese (zh-tw) means Chinese Traditional for Taiwan.
And we simply added Chinese Classical (文言文) and Cantonese (粤语, 廣東話) to the Chinese language family based on the language classifications of Baidu Translator (百度翻译) and Microsoft Translator.
Classical Chinese is still a very important language because it was the language of huge official documents during the dynasties of China, Japan, Korea, and Vietnam.
Thank you very much for your advice, but please refer to fanyi.baidu.com and bing.com/translator to confirm their language classifications.