Sign language (at least ASL) involves a lot of facial expression in addition to using your hands. There's a lot of room to creatively translate the unspoken message in a vocal inflection into signed message.

Subtitles in general, and live captioning especially, avoid editorializing or taking creative license- they're literal translations of words without other cues added in.

One nice exception to this has been the community subtitling work involved in various Taskmaster spinoff series, where explanations for cultural jokes or idioms are added into the subtitles for foreign audiences, especially when the joke is a pun or relies on a mispronounced word to make sense.