Q: iTunes songs local vs iCloud ?

My iPhone is taking up space on my iPhone, around 4GB and I think that it is because some of my music is downloaded to my phone vs being up in the iCloud with ICloud sync.  I would like to get most of this space back.  I don't know of an easy way to do this.

On my iPhone the songs that looks like they are iPhone don't have the iCloud logo.  So, I assume that they were downloaded to my phone.  Yet, the majority of the songs do have the iCloud logo with the arrow pointing down which means that to download to my iPhone, click here.

So, how do I get they songs with no iCloud logo back up to the iCloud and off of my device?

My kids says to swipe and delete the song and it goes back up to iCloud.  Doesn't sound right, so that is why I'm here, to get the right process to reclaim my storage space on my iPhone.

Thank you for your time and attention.