Apple Music and Playlists Maybe I'm missing something here, but my playlist created on my iPhone is not showing up on my iPad. 

Both are up to date, even running on the same network. You would think this would be stored on the cloud, not locally.
I think this is a feature not a bug. different devices you may want to have different playlists for . However that's just my opinion. On the other hand I think if you sync your iPhone and iPad to the same machine and have them both sync all playlists then you should be good to go. However you will have do sync them both all the time to keep them synced lol . Another opinion here. I agree with you. Storing them in iCloud would be good