pigeonhole vs classify

pigeonhole is a noun but classify is not a noun.

Word	Noun	Adjective	Verb	Adverb
pigeonhole	Yes	No	Yes	No
classify	No	No	Yes	No

As verbs, classify is a hypernym of pigeonhole; that is, classify is a word with a broader meaning than pigeonhole:

Other hypernyms of pigeonhole include assort, class, separate, sort, sort out.

pigeonhole (noun)	classify (noun)
a small compartment
a specific (often simplistic) category

pigeonhole (verb)	classify (verb)
treat or classify according to a mental stereotype	arrange or order by classes or categories
place into a small compartment	assign to a class or kind
	declare unavailable, as for security reasons