What languages do the Chinese and Taiwanese both speak?

Both the Chinese and Taiwanese people speak Mandarin Chinese, also known as Putonghua.

However, it's important to understand some nuances:

* "Chinese" is a broad term. It encompasses many different ethnic groups and languages.

* "Taiwanese" is not a single language. While Mandarin is the official language of Taiwan, many Taiwanese people also speak various Minnan Chinese dialects (also known as Hokkien) or Hakka.

Therefore, while Mandarin is the common language spoken by both mainland Chinese and Taiwanese people, they may also speak other languages and dialects depending on their region and background.