I don’t think you can really fit any OSS project into just one of these categories. Any project that is even moderately successful and owned by a company is often most or all of these things.
The trouble you get into with 1–3 vs. 4 is that the “community” can build capacity and competencies for anything the company doesn’t directly try to drive itself and that capacity is usually less limited than the resources of a single company. Eventually the company becomes dependent on that community for the success of 1–3 but needs to maintain a level of ownership greater than its level of participation which can put it in conflict with that community.
I wrote about this a little over a year ago using a park as an analogy https://medium.com/@mikeal/on-corporate-ownership-of-open-source-786ebd15847e#.u74rh1yw7