sun hat vs sunbonnet

sun hat and sunbonnet both are nouns.

Word	Noun	Adjective	Verb	Adverb
sun hat	Yes	No	No	No
sunbonnet	Yes	No	No	No

As nouns, sunbonnet is a hyponym of sun hat; that is, sunbonnet is a word with a more specific, narrower meaning than sun hat:

sun hat: a hat with a broad brim that protects the face from direct exposure to the sun
sunbonnet: a large bonnet that shades the face; worn by girls and women

Other hyponyms of sun hat include pith hat, pith helmet, sun helmet, topee, topi.

sun hat (noun)	sunbonnet (noun)
a hat with a broad brim that protects the face from direct exposure to the sun	a large bonnet that shades the face; worn by girls and women