Person says who we are, nature says what we are. Nature is the source of action but nature doesn't act, the person acts based upon what is proper to the nature of the person. Each human person possesses a human nature, each Divine Person possesses the Divine Nature. Our natures are finite, God's Nature is infinite. "The one infinite nature is totally possessed by three distinct persons. Here we must be quite accurate: the three persons are distinct, but not separate; and they do not share the divine nature, but each possesses it totally."
"... We must not say three separate persons, but three distinct persons because although they are distinct - that is to say, no one of them is either of the others - yet they cannot be separated, for each is what he is by the total possession of the one same nature: apart from that one same nature, no one of the three persons could exist at all. And we must not use any phrase which suggests that the three persons share the Divine Nature. For we have seen that in the Infinite there is utter simplicity, there are no parts, therefore no possibility of sharing. The infinite Divine Nature can be possessed only in its totality."
And here is where it all starts to come together, if each Divine Person is entirely God, why can't we just go ahead and say we believe in three Gods?
"... what is meant by the parallel phrase, 'three men'. That would mean three distinct persons, each possessing a human nature. But note that, although their natures would be similar, each would have his own. The first man could not think with the second man's intellect, but only with his own; the second man could not love with the third's will, but only with his own. The phrase 'three men' would mean three distinct persons, each with his own separate human nature, his own separate equipment as man; the phrase 'three gods' would mean three distinct persons, each with his own separate Divine Nature, his own separate equipment as God. But in the Blessed Trinity, that is not so. The three Persons are God, not by possession of equal and similar natures, but by the possession of one single nature; they do in fact, what our three men could not do, know with the same intellect and love with the same will. They are three Persons, but they are not three God; they are One God."
Nature is the principle of operation, person does what nature allows. And all that leads us finally to the point:
"The operations of the Divine Nature upon the created universe and everything within it are the operations of the Three Divine Persons acting as one principle, not of any one or other of them. Creation from nothing, conservation in being, sanctification, answer to prayer - the work of God in these and all other matters is the work of the Blessed Trinity, the Three-in-One. There is no external operation of the Divine Nature which is the work of one Person as distinct from the others.
"Redemption was not a work in the Divine Nature, but in the human nature which the Son of God made His own; therefore no question arises about the title of Redeemer given to the Son alone, for He alone assumed a human nature and in that nature suffered and died for us. But Creation and Sanctification are definitely operations in the Divine Nature; they are definitely, therefore, the work of the Blessed Trinity and not of the Father alone or the Holy Spirit alone (as Redemption is of the Son alone)."
We must not confuse "appropriation" with reality, appropriation is for our understanding. When God acts, God acts because there are no parts to God. The reason I really didn't want to get into this and preferred to send you to Calvin is that none of this stands alone and every answer raises more questions and Civilization 5 came out last week and I'm kind of having caffeine spasms wanting to play it in every moment of my so called free time. That's wrong.
But do you see the point? Jesus Christ suffered in the flesh because He assumed a human nature and therefore it is easy to say that only the Son died on the cross. At the same time of course the Second Person of the Blessed Trinity chose Mary as His mother because that was an act of the Divine Nature and all external acts of the Divine Nature belong to the Three Persons of the Blessed Trinity, whole and undivided. Internal acts, generation, spiration, processions and missions are of course something else entirely.
Read the bible