Similar to how you can use Chinese characters (traditional or simplified, whatever) to write Vietnamese and Korean and Japanese, as used to happen many years ago.
Mandarin is the most commonly spoken language in Taiwan, partly because the Taiwanese language was more or less outlawed during Martial Law rule from 1949 to 1987. It's also the primary language for education.
Taiwanese is still commonly spoken as well though, especially in southern Taiwan, and is actually becoming increasingly common (partly for political reasons, which are a different topic).
For comparison:
他會曉講台語無？ (Taiwanese)
他會講台語嗎？ (Mandarin)
I also intentionally used 講 instead of 說 for the Mandarin version, since both are valid and it makes it more similar.
A bigger difference would be the standard greeting:
你好 (Mandarin)
你食飽未？ (Taiwanese)