Homer
The shared inheritance
The Iliad and the Odyssey have been transmitted together for nearly the whole of their attested history. Both are in dactylic hexameter; both are divided in the transmitted text into twenty-four books; both stand at the head of the Greek literary tradition and were the foundation of Greek paideia for as long as there was a Greek paideia to speak of. Ancient readers, with rare exceptions, treated both as the work of one poet.
What separates them
The poems do not have the same subject or the same temperament.
The Iliad takes a small slice of the tenth and final year of the Trojan War and makes its subject the wrath of Achilles. It is a poem of battle, grief, honour, and the limits of what a hero can do against fate. It ends not with the fall of Troy but with the ransom of Hector's body and the funeral rites that follow.
The Odyssey takes the years following the war and makes its subject the homecoming (nostos) of Odysseus, the wanderings and adversities he faces, the household at Ithaca and the violent restoration of order there. It is a poem of cunning, endurance and the long work of return. Its hero is recognisably the same Odysseus who appears in the Iliad, but the figure carries weight differently when the surrounding poem is a homecoming and not a war.
The Homeric Question
Modern scholarship — beginning, conventionally, with F. A. Wolf's Prolegomena ad Homerum (1795) and continuing through Milman Parry's twentieth-century work on oral-formulaic composition — has reopened the question of whether the two poems were composed by the same author at all, and whether either or both stand at the end of a long oral tradition rather than being the work of a single literate poet. The question is open. The platform treats it as open.
Why it matters for Virtue & Power
The two poems together set the substrate against which the classical philosophical tradition was written. Plato's worry about Homer's place in education in the Republic is a worry about both poems together; the inheritance of courage, honour and the heroic life that the philosophers receive comes from both, weighted slightly differently in each. To take Homer seriously is to read both poems and to keep them in mind together.