Yes, I believe you are entirely correct.
There was a lot of discussion about all that in the early church obviously. I am not up on it.
According to the Bible, Mary was a virgin when she became pregnant with Jesus - therefore we speak of the virgin birth. This is one thing, Jesus is the result of the Holy Ghost "overshadowing" Mary when she was a virgin and Jesus is not therefore fathered by a human father as would be the normal experience here on earth.
So he is human born in human form from a human mother. He is divine being one fo the 3 persons of God, existant from all time and not made in the way babies of human mothers-fathers are made in the womb. The question about how these two natures - the human and the divine relate to each other within Jesus is something people have discussed and church doctrines (teachings) have developped around.
Personally I don't find it all that important but it seems this is something that set the Coptic church apart a bit (that's a clear, understandable article btw).
The doctrine of the immaculate conception is something els and concerns Mary and whether she was born tainted with the stain of original sin (disobedience of Adam and Eve to the word of God) which otherwise humans are all born with.
Can't believe I am posting all this actually.
Shame the Coptic church is not better known - and its history, fascinating to read about.