What are the two songs that demodocus the bard sings in book 8 about and how do they affect/relate to Odysseus' own situation?

Odyssius  is moved to tears by his songs of the Trojan War and of Odysseus' journey. They hit pretty close to home. Odyssius lowers his emotional fdefences when he is touched by the Bard's music. This will inadvertantly lead to Odyssius revealing his identity. I believe the Bard, Demodocus, sings of a  quarrel between Odysseus and Achilles at Troy.