How do i transfer my own music between iPad and iPhone?

Use iTunes Match

To access your songs and playlists on other devices, turn on Sync Library on all of your devices. When you sign in with the Apple ID that you use with iTunes Match on your iPhone, iPad, iPod touch, Mac, or PC, you associate that device with your account and get access to your music library.

Subscribe to iTunes Match - Apple Support (IN)

Yes, there is a charge to use iTunes Match. That’s why I didn’t suggest that or Apple Music. If you already synced the music to one device using iTunes, you can do it again with the other device.

There is no subscription cost for syncing your own music using iTunes.

Subscribe to iTunes Match - Apple Support

TalkingCatPhotos wrote:

Now I want to put that music on my iPhone but cannot find any way of doing it other than using iTunes from my Windows PC again.

That's how you would have to transfer the music to the phone. You need to use iTunes again. You can’t transfer music directly from one iOS device to another.

since it is on the data store of one Apple device it ought to be possible to transfer the files directly between the two devices.

But it’s not possible.