I have a subscription to Music, and I see references to purchases. Can anyone explain this, please

With an Apple Music subscription, you only lease the music to play on Apple-approved devices. That music is copy-protected (you cannot burn it to a CD) and will vanish if you let your subscription expire or cancel it. You can still purchase music with or without an Apple Music subscription in which case you own that music can do what you want with it for as long as you want (within the copyright restrictions).