cane vs walking stick

cane and walking stick both are nouns.

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

As nouns, walking stick is a hypernym of cane; that is, walking stick is a word with a broader meaning than cane:

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

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