Professor Stephen Bainbridge asks "If corporations are not people, then what are they?" Although I hesitate to cavil over diction, I do think the question is more properly framed "If corporations are not persons, then what are they?"
The word "people" usually refers to human beings, being derived from the Latin word populus, which generally refers to humans. "Person" is derived from a different Latin word, persona, which refers to a thespian's mask and by extension to the character. It could also refer to human or beings having legal rights. Hence the famous title SPQR is an initialization of Senatus Populusque Romanus (the Senate and the Roman People (not Persons)).
Not shrinking from stating the obvious, the California Assembly has solemnly declared "Corporations are not people but, instead, are entities created by the laws of states and nations". AJR 22, Cal. Stats. ch. 69 (July 12, 2012). At the same time, the legislature has affirmed in numerous statutes that corporations are indeed persons, including California Corporations Code Sections 18 (“‘Person’ includes a corporation as well as a natural person”); 15901.02(y) (“‘Person’ means an individual . . . corporation . . .”); and 25013 (“‘Person’ means an individual, a corporation . . .”).