sweet pepper plant vs capsicum

sweet pepper plant and capsicum both are nouns.

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

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

sweet pepper plant: 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 plant include capsicum pepper plant, pepper.

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