Yup. And there is a very great deal of evidence - specific memory markers such as repetitions of "rosy-fingered dawn" for example - that both poems are exactly that. The controversy these days mostly centers around the question "Were there two Homers?", based on subtle differences between the Greek dialect used in the oldest available copies of the respective works. That's way outside my paygrade but my last Classics professor said he thinks there's a good chance there probably were.
Obviously Homer did not write the two epic poems.
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It was William Shakespeare.
My Greek prof thought that one was the original and the other an edited version by a later hand. Not really “two Homers”, just a Homer and an Editor.