bell pepper vs capsicum

bell pepper and capsicum both are nouns.

Word	Noun	Adjective	Verb	Adverb
bell pepper	Yes	No	No	No
capsicum	Yes	No	No	No

As nouns, capsicum is a hypernym of bell pepper; that is, capsicum is a word with a broader meaning than bell pepper:

bell pepper: plant bearing large mild thick-walled usually bell-shaped fruits; the principal salad peppers
capsicum: any of various tropical plants of the genus Capsicum bearing peppers

Other hypernyms of bell pepper include capsicum pepper plant, pepper.

bell pepper (noun)	capsicum (noun)
large bell-shaped sweet pepper in green or red or yellow or orange or black varieties	any of various tropical plants of the genus Capsicum bearing peppers
plant bearing large mild thick-walled usually bell-shaped fruits; the principal salad peppers