I like to say a person is a human, and a human is a person. And that is true; it is also not wholly true. Every human is a person, to be sure, but it should be said that not every person is necessarily human.
Every time I see (or say) something like "human and person are synonyms" I have a tick in the back of my mind objecting to the simplicity. Here is the problem:
Holy, Holy, Holy! Lord God Almighty! Early in the morning our song shall rise to Thee.
Holy, Holy, Holy! Merciful and mighty!
God in three persons, blessed Trinity!
God exists in three persons. However, God is not three people.
The dictionary definition of the word person is human, individual; that is, human and person are, indeed, synonyms. A subset of this is "character" as in a play or story. A special use of the word person occurs in Christian theology to describe what the OED calls God's "modes." We use the word like character in that sense. The triune nature of God is difficult to express in words; it is such a mystery. So, our words -- mode (as though he's a machine), character (as though we're in a novel), person (as though he's a man) -- contain this unknown aspect when we speak of him. Even the pronoun him is a little off, though God uses it often to refer to himself. He is not really a "he" at all. Neither is he a she; God is neither male nor female.
We use other words with the same difficulty -- describing physical aspects that he doesn't actually have, for instance. My kids often wonder how big God is. My answer is usually that he is very big -- infinitely so -- and also not big at all. That is, he's not in the category of big and small things. He is so far beyond our limited experience and understanding; he is wholly other.
A human is a person; as soon as a new human exists, a new person exists. Personhood is not a mysterious extra category reserved for independently-thinking, already-birthed, self-aware humans.
I bring this up because what constitutes a person is often questioned when talking about the right to life. The argument is that one needs to be more than simply human to be considered a person; person is a subgroup of human with certain distinguishing characteristics, such as consciousness and personal preferences. This is false. A human is a person; as soon as a new human exists, a new person exists. Personhood is not a mysterious extra category reserved for independently-thinking, already-birthed, self-aware humans. Person and human are synonyms.
Except when they're not. There is one Person who is not a human. We describe some of his mysterious triunity with the word "person" because of his likeness to a character -- like in a story. This would seem to indicate that what constitutes a person is itself mysterious, but it doesn't. God is mysterious. That he is three but only one is mysterious. That he never came into existence as we do but has always existed is mysterious. That he has always been three person-, character-, mode-things though one being and bodiless is mysterious.
For while we were still weak, at the right time Christ died for the ungodly. For one will scarcely die for a righteous person—though perhaps for a good person one would dare even to die— but God shows his love for us in that while we were still sinners, Christ died for us.
It's not wholly related, but I can't write that last sentence without Jesus coming to pen. God in three persons without a body forever until one day a young virgin became pregnant with the Son of God. Becoming fully human, he still to this day has the body of a man. With this body he lived among us, being unborn and then born and growing from childhood to an adult. And with this body Jesus bore the guilt and penalty for the sins of many -- for all who had, did, and would ever trust in his name. And he died with this body, and rose back to life with this same body. He lives forever as the God-man in this body.
Men and women saw him, touched him, smelled his sweat. We have their written accounts of him and look forward to seeing him too. He became a physical person for us. It's almost too hard to believe. We will literally see him. People have seen God.