Is it possible that you have the Apple Music subscription active on one the iPad and not on the iPhone? Or did you maybe manually sync the song via iTunes to your iPhone but not to the iPad? Seems like the iPad uses the protected Apple Music version while the iPhone uses your own version.
In any case, just export the song from Stage Traxx and Airdrop it to your iPad. That will also transfer all song specific settings you made and the problem is solved.