“Chinese” can refer to a variety of languges in China.

It could refer to 中文 --> Chinese Characters
It could refer to 国语/普通话 --> National Language / Mandarin
If its overseas, the English term “Chinese” could also refers to the overseas lingua franca, which histoically had be Taishanese, but now is Cantonese, and slowly being replaced by Mandarin as more non-Cantonese Chinese people emigrate.
Cantonese-Chinese people usually just ask “識唔識白話” (“Do you speak Cantonese?” in Cantonese), then if no response, immediately switch to Mandarin “普通话？” (“[Do you speak] Mandarin?”)

Cantonese, [could be refered to as any of the following: 廣東話/廣州話/廣府話/粵語/白話], is a variety of Chinese known as Yue-Chinese. In Chinese, it’s referred to as a “dialect”. It’s only used in Hong Kong and Guangdong, but overseas it was, and still kinda is, the lingua franca due to most of the diaspora being from there.

Traditional 繁體 is the older set of characters that has been in use for… idk how long but a very long time.

Simplified 简体 is the newer set of characters, standarized by the PRC Government after they won the KMT-CCP Civil War. ROC (aka Taiwan) didn’t adopt these simplifications. Hong Kong also didn’t adopt the simplifications afaik.

-Am a Native Speaker of both Cantonese and Mandarin, currently residing overseas