Have you noticed that some Bibles say both Immanuel and Emmanuel while others only say Immanuel?
So what's the difference?
They are exactly the same word with the same meaning, "God with us."
But they are spelled differntly. One has an "I" while the other starts with an "E".
Which one is right?
Well, both can be called "right", but, in my opinion, one is more accurate than the other.
It comes to this: Immanuel is the English translation of the Hebrew "עמּנוּ אל" (‛immānū'ēl) and Emmanuel is the English translation of the Greek "Ἐμμανουήλ" (Emmanouḗl) which is a translation of the Hebrew "עמּנוּ אל".
In my opinion, which you can disagree with without recourse, "Immanuel" is the more correct term as it is a direct translation of the original Hebrew, whereas "Emmanuel" is a translation of a translation.
So, there you go.
But, in all of this, DO NOT MISS THE POINT:
In the beginning was the Word, and the Word was with God, and the Word was God. He was in the beginning with God. All things were made through him, and without him was not any thing made that was made. In him was life, and the life was the light of men. The light shines in the darkness, and the darkness has not overcome it... And the Word became flesh and dwelt among us, and we have seen his glory, glory as of the only Son from the Father, full of grace and truth.
(John 1:1-5,14 ESV)
Jesus IS Immanuel; God with us!