It's only different because
Godhead is used instead of Trinity, and the nature of God has been revealed to us throughout the Bible. From beginning to end.....hundreds of verses. Someone decided to give that name to the fact of God's nature as it has been revealed. The Godhead speaks of God's nature. And our Lord and Saviour makes it clear....And, I might add, uses the same word that is used in Genesis concerning making man in
OUR image. Same with US and WE.
"WE will come to him, and make OUR abode with him." How exactly do the Father and Son come to dwell in them but through sending the Holy Spirit?
John 14:23, "Jesus answered and said to him, "If anyone loves Me, he will keep My word; and My Father will love him, and We will come to him, and make OUR abode with him."
Now, if you can't see the ONE God in three distinct "persons", there is something wrong with you. You see the "I" for Jesus, "Father", and "he" for the Holy Spirit (Comforter).
John 14:16 And I will pray the Father, and he shall give you another Comforter, that he may abide with you for ever;
John 14:26 But the Comforter, which is the Holy Ghost, whom the Father will send in my name, he shall teach you all things, and bring all things to your remembrance, whatsoever I have said unto you.