hard hat vs helmet

hard hat and helmet both are nouns.

Word	Noun	Adjective	Verb	Adverb
hard hat	Yes	No	No	No
helmet	Yes	No	No	No

As nouns, helmet is a hypernym of hard hat; that is, helmet is a word with a broader meaning than hard hat:

hard hat: a lightweight protective helmet (plastic or metal) worn by construction workers
helmet: a protective headgear made of hard material to resist blows

hard hat (noun)	helmet (noun)
a lightweight protective helmet (plastic or metal) worn by construction workers	a protective headgear made of hard material to resist blows
a worker skilled in building offices or dwellings etc.	armor plate that protects the head