"Linguistic categories" are categories (a general term) found in language. There is no definitive list of such categories. You appear to want to exclude phonetic and phonological categories, but including or excluding P-categories does not change the meaning of "category", it just narrows the set of posited categories.
"Categories" are conventional names that correspond to posited "thing" concepts, for example "noun" refers to very many specific words in many languages, analyzed from a certain perspective; "verb" is a concept that subsumes a different set of words. There are many categories of categories, and also theories of what the actual categories are. "Noun" might be a syntactic category, or it might be a morphological category – it depends in part on what your theory of grammar is (there are theories that don't have a thing "morphology": there are also theories that don't have "phonetics" as a thing).
In Aspects-model transformational grammar, "movement" was not a "thing" in the theory, it was epiphenomenal – rules written in a certain way can be said to be "movements". That theory had entities like "N", "NP" (actually, features), and other things that were about how rules are written (for example "variable"). The theory also had things termed "rules". At certain stages, movement became a "thing", and rules per se became epiphenomenal. Every theory has some number of "things" that it says exist in language, and when two or more things are said to be "similar" and distinct from some third thing, you have a category. Then you can ask, what are the categories, and how are they defined? Furthermore, I'm presenting you with a conventional generative-grammar ontology which has (at least ideally) pretty crisp categorization, but there are theories of language that don't divide things sharply into well-defined categories.
The Wiki page on "grammatical category" is far from complete. In addition, it only addresses a narrow sense of "grammar" that focuses on syntax and morphology but not phonetics, phonology and semantics.