Have been looking for a taxonomy of museums, galleries, etc. but no luck. Even formulating a suitable search query on Google, which nowadays is so powerful that it finds me almost anything with just a few tries, seems a tricky business. However, in the process I stumbled upon the Fractal Taxonomy of Museums, which at least gives a long list of different types and aspects of organisations.
Center for the Future of Museums: The Fractal Taxonomy of Museums