Because you have tagged this with "Suzanne Vega" I assume that you are asking about her song "Calypso."
This song is one that is told from the point of view of Calypso as she lets Odysseus leave her island. In that sense, it is very different from Homer's poem because Calypso is the main character.
The facts of the song fit well with what happens in Homer's epic. Calypso found Odysseus when he was drowning and she has held him for years, but now she is letting him go. He will be sailing away and she will be helping him sail away. In all of these facts, the song is true to the story.
The major difference is that Calypso seems more willing to let Odysseus go in this song. She says that she will not ask him to return and she implies that she was willing to let him go. In Homer's telling, she had to be ordered to let him go and, even then, she offerred him immortality if he would stay with her.
This makes sense given that the song is from her point of view. She is trying to make herself look better as she tells the story. She is trying to make herself look strong, magnanimous, and not desperate for his company.
So the major difference is that this song is from Calypso's point of view and therefore tries to show her in the best possible light.