Interesting question! A song is exactly what you might think it is: a piece of music that is singular (in other words that can stand alone), vocal or instrumental, and that might have lyrics or words in it. An anthem is actually just a type of song. It is generally very rousing or uplifting (inspiring might be another word?). It can also be the song that is officially adopted by a country as its national song (national anthem). Hope that helps!

An anthem is a song for celebration. Like a national anthem (celebrate country) or sports anthem. A sports anthem may just be a song with a certain message in it like 'We Are the Champions'.