A song is a set of lyrics accompanied by a tune. A good song text should provide an adequate amount of emotion while not overpowering the listener. However, not all songs are created equal. Some are mediocre and are more about the melody than the lyrics.
A lyric is a short poem used to convey emotion. The word "lyric" derives from the Middle French word "lyrique". Traditionally, a lyre is a small stringed instrument which is played while singing.
The lyric is usually a verse, but can also predate the tune. A lyric is a combination of the eloquent words and the technical marvels of rhyme, alliteration and meter. A lyric is not only a creative expression, it's also the intellectual property of the lyricist. The best lyric can reference the feeling as well as the melody.
The best lyric is the most evocative. It's a good idea to write down a song's most memorable lines to later recall. It's also a good idea to read other artists' lyrics to gain new ideas. Some of the best lyrics have been written by multiple lyricists. A bad song is one that merges feelings into one.
A lyric is a complicated task, but with a little patience, the rewards are well worth the effort. A good lyric can elevate a simple melody to a work of art. You may even want to consider a songwriting course. It will pay dividends when you're ready to churn out your own masterpieces.