Using the word 'kind' for a category

Kind means type, among other things. Here's a chart of the PIE root *ɡenə- (from which all senses of kind come, including the one that means gentle).

(Note, parenthetically, that words for ruling classes develop good meanings in time, whereas words for commoners -- like mean and common, say -- don't.)

However, the fact that kind means type doesn't affect the grammar of the two words. Being a kind is a predicate, by itself, and kind (or, for that matter, type) should not be thought of as sets to which things "belong". That's unnecessary complication.

There are idioms like kind of /'kayndə/ (He's kind of shy). Type of doesn't work here: *He's type of shy. But they do both work in constructions like

• What kind/type of idiot would do that?

though kind is more idiomatic and type is more formal here.