Documentation uses payload when it should be claim

[samholmes]

The JWT spec calls this "payload" a "claim". You're documentation should use this convention to not confuse the subject.

[MichielDeMey]

Correct, the body consists of one or multiple claims.
However, since - beside the registered claim names - you can add any claim (JSON property) you want, it does make sense to name it 'payload'.

Most JWT packages I've used name it 'payload', some use 'claims'. It's up for discussion.