Apple has a detailed explanation of the differences between Apple Music and iTunes Match in regard to your music library, but they can be summed up more easily.
iTunes Match matches your songs’ acoustic fingerprint against Apple’s Music catalog to find the perfect match while Apple Music only matches against your song’s details (such as name, artist, album). This means iTunes might choose a different version or recording of some of your songs instead of your original ones.
iTunes Match automatically uploads songs which can’t be matched. Apple Music doesn’t allow uploading of songs which are not in the music catalog. Uploading is important if you have rare titles you want to keep.
iTunes Match let’s you download DRM-free (freely copyable) music of your matched songs while Apple Music only let’s you download DRM-protected (copy protected) music. The quality for both is the same (256 Kbit/s AAC).
iTunes Match lets you only listen to your music while Apple Music lets you listen to all the music Apple has in its music catalog. Both are available on all your Apple devices and allow for streaming and downloading.
So iTunes Match is the choice if you want to have your meticulously built music library accessible on all devices without manually syncing parts of your library to your storage constrained devices. And then you can top it off with Apple Music if you like more music but don’t want to buy anymore.
Apple-Music-only is for people who don’t have an extensive library of rare music and are fine with conveniently getting the Apple music catalog as it is.
It seems Apple has retired iTunes Match in favor of Apple Music. While I’m still able to restart my canceled iTunes Match subscription, there doesn’t seem to be a way to start a new subscription for first-timers.