I hope that these "fixes" - re-installing the iTunes Music player or a hard restart (home and power buttons) - really do resolve these problems fully for joseph and NEKO.
That said, though, I have tried both of these fixes with my iPhone (a 5s) and have found them to work only temporarily. Music playback will function better for a few days, but similar problems will then occur again. The problems are (I think) less severe and persistent than they had been: a simple re-start will then result in music playback working OK for some period of time (perhaps a day or so).
Also, to be very clear to Apple employees who may read this comment, the problem does not at all appear to be the audio files. These issues occur across a wide variety of songs, and the problems don't always occur in the same places within songs. I have verified that sometimes these playback problems occur with songs that I've recently downloaded through iTunes using my Apple Music subscription. In other words, if Apple is claiming that audio files are the problem, then Apple is saying that it provided with me with damaged audio files through Apple Music / iTunes within the past few weeks.
The point from many others in these comments stands. Apple introduced this problem with recent iOS updates. I never had any of these sorts of problems playing back music until a recent iOS update. I think it was sometime after installing iOS 11.4 for me. I have also now occasionally noticed similar problems with my iPad (an iPad Air 2).
Apple needs to acknowledge that it caused this problem, apologize, and fix the bug.