Songs play, but apps can be played. Therein lies the difference between these two data types, which are often distributed by the same stores.
Songs that are apps -- or are delivered by apps -- have several advantages (as noted years ago): Users can play them like video games, connect with other people who are listening, tag them to geographical locations, discover similar music, create playlists out of your face, make songs cry, and so on.
However, delivering music as apps brings another key advantage, as JY Design points out: You can re-download apps to your smartphone, computer, or tablet for free, should you mistakenly delete or otherwise lose track of them. Meanwhile, traditional music download stores leave you to do that on your own, whether that means re-downloading them from bit torrent or something else.
He writes (slightly edited),
If Apple wants to best Amazon in cloud music wars, it needs to do something uniquely Apple... Can you imagine losing your only copy of an app along with your iDevice, only to be told you had to re-buy that app? The music industry would love it if you had to re-purchase and re-download your music catalog every time your hard drive died or your kid lost her iPod. But that's asinine. The app purchasing model let the consumer-friendly online-purchase genie out of the bottle. Buy once, re-download when you need to, is the new norm.