What is the difference between playlists and downloaded music

A playlist is just a list. The process is the same in many circumstances, not just iTunes. You have a library of (say) audio recordings. Then you construct a playlist using some of them: you can select the ones you want, you can change the order, and play your chosen songs using the playlist. If you remove a song from the playlist it does not delete it from the library (iTunes offers, in the right-click menu, the option either to remove a song from the playlist or delete it from the library). The playlist is just a collection of pointers.

Now I see your confusion. I never paid any attention to the option of downloaded music in the music app. When I tap that selection, I get the same options of playlists, artists, albums and songs. In this situation, I do not know the difference between playlists and downloaded music. The one thing I see now when I go back to the downloaded music option is that it says at the top “showing only music on this phone”. I don’t stream music from iCloud so that may show up in the initial library setting for playlists and the other options. Hopefully, someone with more knowledge on this will reply.

Downloaded music would be all the music on your phone. Playlists would be lists of selected music. I have a lot of my music on my phone and I have it divided into several different playlists depending on what type of music I want to listen to. That way, I don't have to play every song on my phone just to listen to the ones I want at the moment.

With Apple Music songs (as opposed to songs in your Library you have bought or downloaded) you can create a playlist specifying songs from the Apple Music library which you would then stream or download, depending on your settings.

If you sync this playlist to the phone, the Apple Music songs which you had downloaded to your Mac won't be on your phone until you download them again - you can't transfer Apple Music songs from one device to another, you have to download them separately on each device.

From what you describe it may be that the playlist is downloading the songs again, so that it would only download the songs which were in the playlist and these would become downloaded.

This Apple Help page may clarify matters:

https://support.apple.com/HT207542