common pea vs pea plant

common pea and pea plant both are nouns.

Word	Noun	Adjective	Verb	Adverb
common pea	Yes	No	No	No
pea plant	Yes	No	No	No

As nouns, pea plant is a hypernym of common pea; that is, pea plant is a word with a broader meaning than common pea:

common pea: plant producing peas usually eaten fresh rather than dried
pea plant: a leguminous plant of the genus Pisum with small white flowers and long green pods containing edible green seeds

Other hypernyms of common pea include pea.

common pea (noun)	pea plant (noun)
plant producing peas usually eaten fresh rather than dried	a leguminous plant of the genus Pisum with small white flowers and long green pods containing edible green seeds