Is Cthulhu REALLY a Great Old One?

Here's something that has always bothered me. In H.P.Lovecraft's "The Call of Cthulhu", there's the following passage:

They worshipped, so they said, the Great Old Ones who lived ages before there were any men, and who came to the young world out of the sky. Those Old Ones were gone now, inside the earth and under the sea; but their dead bodies had told their secrets in dreams to the first men, who formed a cult which had never died. This was that cult, and the prisoners said it had always existed and always would exist, hidden in distant wastes and dark places all over the world until the time when the great priest Cthulhu, from his dark house in the mighty city of R’lyeh under the waters, should rise and bring the earth again beneath his sway. Some day he would call, when the stars were ready, and the secret cult would always be waiting to liberate him

Boldface and underlines are mine.Cthulhu, who in later texts is recognized as a one of the Great Old Ones, is referred to here as being a "great priest". Does this mean that Cthulhu is a priest OF these Great Ones, or is he one of the Great Old Ones, and his position among them is that of a Priest (i.e. - he's the cleric of the party)?

Either way, it is is an interesting take on things. If he's a priest who venerates these Great Old Ones, he's subordinate to and separate from them, and the Great Old Ones (of which later writers have constructed an entire pantheon) are unknowable, godish beings who we have never really met. If is a priest among the Great Old Ones, what do these Great Old Ones worship?

Hang on, it gets even more interesting in the next paragraph.

Meanwhile no more must be told. There was a secret which even torture could not extract. Mankind was not absolutely alone among the conscious things of earth, for shapes came out of the dark to visit the faithful few. But these were not the Great Old Ones. No man had ever seen the Old Ones. The carven idol was great Cthulhu, but none might say whether or not the others were precisely like him. No one could read the old writing now, but things were told by word of mouth. The chanted ritual was not the secret—that was never spoken aloud, only whispered. The chant meant only this: “In his house at R’lyeh dead Cthulhu waits dreaming.

So no one has ever seen the Old Ones, but here's a statue of Cthulhu, which we know from the later in the story is a pretty fair representation of his titanic majesty.

So it seems, from this reading, that the entire later industry of Great Cthulhu as one of a pantheon of elder eldritch beings may be off. His fictional worshipers, as well as later real-world chroniclers, have confused and conflated the two, promoting the priest to the godhood itself. Of course, all of this is from a highly unreliable narrator, a mad and degenerate worshiper of these Great Old Ones, On the other hand this is a primary source, THE primary source, of Cthulhu lore.

Anyone have an theory on this?

More later,