To me it also seems that poems are more about feelings sometimes in a more abstract way. Words used are very flowery and descriptive or dark and many times without a plot or story line.

Song lyrics in many cases have a story to tell, a plot, a character, a setting, a conclusion or a moral to the story. Not in all cases, but in many cases, especially in country and folk music. A lot of Bob Dylan's songs were about characters and stories told through songs.