difference between a project's business case and project initiation document?

A project initiation document(PID), is a document that is prepared prior to implementation of the project. It contains:
-The Business justification/case
-The roles and responsibilities of members
-the risks of the projects
-the constraints of the project(scope,time,cost)
-the resources needed

Whereas the business case is in the PID, it states the purpose of the project. However it is important to distinguish the business objective and project objective, whereby what is trying to be achieved by the project isn’t necessarily what is the business objective