Syncing music library requires a subscription to Apple Music?

Even if you have iCloud sync turned on and are syncing everything from your Mac to iCloud, and have iCloud turned on on your devices, if you don't pay to subscribe to Apple Music then the music you own in your music library on your Mac doesn't automatically sync to your other devices?

I wanted to get a song from my Mac onto an old iPhone 6 Plus and it seems I needed to connect the iPhone to my Mac and when it appeared in the Finder sync that one song over manually. Is that right?