[hummingbird42]

One of the songs in my playlist has a little gray triangle with a picture of what looks like an iPad in it. It's in the right hand corner right above the three red dots. What does it mean?

[Tartarus]

It means you've saved that playlist for offline use.. All songs are locally stored on your iPad

[hummingbird42]

Thanks! It's only by one random song in the middle of the playlist. So, is just that song saved for offline use? Or the whole playlist?

[Tartarus]

The whole playlist. You have saved that particular random song earlier individually.

There are two scenarios for offline saving:
1 Saving an entire playlist, album or artist will leave an iPad or iPhone sign on only the album cover up top
2 Saving an individual song will leave an iPad/iPhone sign on the cover of that particular song.

Now, if that individual song is part of an offline album/playlist it will keep that sign.

If you go to Settings > General > Storage & iCloud Usage > Music, you will see which songs are saved on your iDevice. Also, if you choose to show "Music Available Offline" you will see which songs are available offline as well.