walking stick vs cane

walking stick and cane both are nouns.

Word	Noun	Adjective	Verb	Adverb
walking stick	Yes	No	No	No
cane	Yes	No	Yes	No

As nouns, cane is a hyponym of walking stick; that is, cane is a word with a more specific, narrower meaning than walking stick:

Other hyponyms of walking stick include supplejack.

walking stick (noun)	cane (noun)
any of various mostly tropical insects having long twiglike bodies	a stiff switch, used to hit (usually students) as punishment
a stick carried in the hand for support in walking	a stick that people can lean on to help them walk
	a strong slender often flexible stem as of bamboos, reeds, rattans, or sugar cane

walking stick (verb)	cane (verb)
	beat with a cane