The the term "person" and what it signifies, as it has been handed down to Western civilization through the Christological and Trinitarian deliberation of the early Ecumenical Councils, is primarily an ontological term that signifies a specific mode of being. A person is an individual substance of an intellectual nature. Or, to make more explicit what it means to be a person, we can say that a person: (1) possesses a substantial existence, not an accidental existence; (2) possesses a complete nature; (3) exists per se, possessing the fullness of its existence, its nature, and all its powers and acts; (4) separate from others, meaning that the primary sense of the term "person" refers to a specific individual rather than something universal, though we can use the term analogically to include all types of beings whose nature and mode of being render the individuals of said nature persons; (5) possessing an intellectual nature, i.e. possessing intellect and will.
Any use of the term person that does not fall under this specific definition is analogically related. For example, a legal person is treated as is it possessed a separate, substantial existence, possessing an intellect and will and being the full and sole possessor of all its powers and actions. A corporation, for example, does not possess any of the attributes of a person, but it is treated as such for the purpose of the law. This can be fine and necessary for a well running legal system (though I am myself opposed to corporate personhood). But if we loose site of the primary meaning of the term "person," the one from which any and all analogical uses stem, then we have lost sight of something very important to the proper understanding of human nature and the reality of the world.