What is a commentary? UPDATED

And how the Nyāyamañjarī and the Seśvaramīmāṃsā do (not) fit the definition

What makes a text a “commentary”? The question is naif enough to allow for a complicated answer. First of all, let me note the obvious: There is not a single word for “commentary” in Sanskrit, where one needs to distinguish between bhāṣyas, vārttikas, ṭippanīs, etc., often bearing poetical names, evoking Moons, mirrors and the like.