Google photos and Synology photos "free up space" features

Backed up my mom's phone using Synology photos to the family NAS, and also to Google photos.

If I "free up space" in Google photos does it affect the Synology photos saved on the NAS?

There's a "deletion settings" in Synology that states "only delete on device" or "delete on device and Nas"

So that's different than "free up space" right?

That's a manual tap and delete type thing setting?

Freeing up space in Google photos will NOT affect Synology backups?