sweet pepper vs capsicum

sweet pepper and capsicum both are nouns.

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

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

sweet 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 sweet pepper include capsicum pepper plant, pepper.

sweet pepper (noun)	capsicum (noun)
large mild crisp thick-walled capsicum peppers usually bell-shaped or somewhat oblong; commonly used in salads	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