Interesting question.
The Project Charter is a formal record of a project. The inputs are Business Documents, Agreements, EEFs, and POAs. The result of these documents, of which many may be external, creates a new document, The Charter, but the charter is a document that is essentially locked; it should not be changed.
The Charter is also sometimes considered redundant to the Scope, but at a higher level.
A Business Case could have been a project by itself, which would have had some kind of Charter too.
Throughout the PMBOK, The Charter is described as documenting something. It is a direct result of a specific process.
Further, Project Documents have a tendency to get changed, whereas a Charter would not, and thus probably should not specifically be listed as a project document. In my opinion, The Charter is a locked project Document, it is used as a project document, but does not get updated or changed. I think that is the big difference.