Apparently Android indexes mp3 files on an micro SD card after you insert it into your phone. All music players show the same set of indexed music files.
Unfortunately, the indexing can sometimes be incomplete. When I started up a music player, -- either the Samsung Music Player or the Google Music Player, it did not matter -- I saw some of my songs, but not all of them. I could browse into the folders on the micro SD card and play each of the missing files, but I just could not find them inside the music player.
My files are inside the "Music" folder, and I do not have a file named ".nomedia" in there.
So I decided to try to get my phone to re-index the SD card. Here are my steps:
1. I turned off the phone.
2. I removed the micro SD card.
3. I restarted the phone to let it know that I no longer have a micro SD card plugged in.
4. I turned off the phone again.
5. I re-inserted the micro SD card.
6. I restarted the phone to let it know that I now have a micro SD card plugged in again.
Sure enough, Android started scanning the micro SD card to index files on it. At first I was a little nervous, because the music players where showing even fewer files than before. But after a while, all mp3 files are found, and my problem is now solved.