private vs static private

There's no specific use case, just a general one. I have a use case, but it's fairly specific to something I'm working on. I've created a small library that provides the ability to share private data between classes. It's based on this thread I started:

The trouble came when using it to work on another library. The first library (cfprotected) uses a private field as a container for the shared data. I need both the instance and the static objects to have a shared container. It would be easier if they both had a shared container of the same name. This would make it easier than having to remember 2 different container names. That's how I ran into this issue.