Is it common for universities to have multiple boards (eg, a General Planning Board, a Finance Board, etc.) and what is the typical name for these?
I know that you ask preferably for the US and UK, but as a side note, this model is standard for universities in Switzerland (and presumably other German-speaking countries). These are typically called Kommissionen (which translate to commissions or I think more appropriately committees). Contradictory to your example, these committees are not exclusively staffed with professors. They are composed of a president and representatives of all levels of the university employees and students: faculty, "intermediaries" (postdocs, lecturers), admin/technical staff, and students.

Here is the list of the different committees from the University of Zurich. It includes the research committee, the ethics committee, the disciplinary committee, etc. The other universities of the country are organized in a very similar manner.