You answered your question that Mary gave birth to Christ, full stop. This same Christ who walked the earth and was the child of Mary is the God-man. Mary gave birth to the one cohesive person who is Jesus Christ. The second hypostasis of the Trinity entered her womb and took flesh of her and made it his own. This is called the hypostatic union.
Nestorianism believes that Christ is a duality of persons. The human person born of Mary and second person of the Trinity who occupied this mere man Jesus as a temporary receptacle.
The canonical epistles of Cyril to Nestorius presented at Ephesus 431 AD explain the Orthodox understanding:
For we do not say that the nature of the Word was changed and became flesh, or that it was converted into a whole man consisting of soul and body; but rather that the Word having personally united to himself flesh animated by a rational soul, did in an ineffable and inconceivable manner become man, and was called the Son of Man....Because the two natures being brought together in a true union, there is of both one Christ and one Son; for the difference of the natures is not taken away by the union, but rather the divinity and the humanity make perfect for us the one Lord Jesus Christ.
Confessing the Word to be made one with the flesh according to substance, we adore one Son and Lord Jesus Christ: we do not divide the God from the man, nor separate him into parts, as though the two natures were mutually united in him only through a sharing of dignity and authority (for that is a novelty and nothing else), neither do we give separately to the Word of God the name Christ and the same name separately to a different one born of a woman; but we know only one Christ, the Word from God the Father with his own Flesh....
Besides, what the Gospels say our Saviour said of himself, we do not divide between two hypostases or persons. For neither is he, the one and only Christ, to be thought of as double, although of two (natures) and they diverse, yet he has joined them in an indivisible union, just as everyone knows a man is not double although made up of soul and body, but is one of both. Wherefore when thinking rightly, we transfer the human and the divine to the same person....And since the holy Virgin brought forth corporally God made one with flesh according to nature, for this reason we also call her Mother of God, not as if the nature of the Word had the beginning of its existence from the flesh.