iTunes internet audio stream issue

Hello all. Thank you in advance for your answers!

I like listening to radio streams (local radio stations) directly from iTunes. I have a playlist specifically for radio stations. My problem is that some stations from my playlist show up in the songs sections, while some don't. I have not been able to figure out why - I add them all in the same way:

- On the website of the station: copy audio address

- In iTunes: File> Open Stream > paste

Then some of the streams I open automatically save to my playlist and also don't show up in main music tab, but some streams aren't automatically added and I have to manually click on the playing stream and click "Add to playlist" - meaning the stream also shows up in the music tab.

On what basis is this determined? How can I remove the streams from the music tab, without removing it from my playlist.

Thanks!