crown jewels vs diadem

crown jewels and diadem both are nouns.

Word	Noun	Adjective	Verb	Adverb
crown jewels	Yes	No	No	No
diadem	Yes	No	No	No

As nouns, diadem is a hyponym of crown jewels; that is, diadem is a word with a more specific, narrower meaning than crown jewels:

crown jewels: regalia (jewelry and other paraphernalia) worn by a sovereign on state occasions
diadem: an ornamental jeweled headdress signifying sovereignty

Other hyponyms of crown jewels include crown.

crown jewels (noun)	diadem (noun)
regalia (jewelry and other paraphernalia) worn by a sovereign on state occasions	an ornamental jeweled headdress signifying sovereignty