Some projects are managed by a community including multiple companies. Others are dominated by a single company or individual. I've heard the term "community project" applied to the former. I don't know if we have a term for the latter.
I agree with another poster here who suggested that re-defining Open Source risks turning into a "No true Scotsman" scenario. I often hear this argument used to justify people going with a proprietary solution (like Windows phone), because the competing solution(s) (like Android) are not "open source enough." It's BS.
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