While she keeps more than just slips of paper (or index cards) in it, Twyla Tharp definitely falls into the pattern of creative collection related to the zettelkasten tradition.

Project notes can be kept in folders either inside or outside of the zettelkasten itself, but they technically shouldn't be a permanent part of it. Perhaps it's better to think of them as a workbench or play space for ideas as they're forming into a finished piece of writing. Once the piece is done, the play space has served its purpose and can be cleaned up.

My equivalent, as best as I can tell, is:

• Permanent notes (atomic, linked concepts) = Notions
• Temporary notes (half-formed thoughts, links, snippets, etc.) = Notes
• Temporary notes initially, which later become permanent notes = Ideas (see later comment about why)
• Admin notes (projects, tasks, meetings, etc.) = Work notes

Similar to how I've come to think of my "admin" or "operational" notes. They're instrumental in that they serve a purpose that is usually about moving some project forward.