"download" is a simple and clear word, but not in Apple Music
Seems like Apple is not interested on a creating a good experience with the downloaded songs. You are 100% forced to be online to have a good experience. So many errors, so many issues, weird noises, incomplete songs, failures to play if you are offline, on a plane, in the airport, without access to network.
A downloaded song should just play, simply that: just play. But apparently Apple finds that difficult to achieve.