Delete Photos on iphone vs icloud

Deleting a photo deletes it from everywhere. What you probably want is offloading the photo storage to iCloud:

1. Tap Settings > [your name] > iCloud > Photos.
2. Turn on iCloud Photos.
3. Select Optimize iPhone Storage to save space on your device.

See here for more: Manage your photo and video storage

iCloud is a syncing service, NOT an archive. If you save photos in the cloud, which it sounds like you do, when you delete a photo on any iOS device using the same Apple ID, they also delete from the cloud.

You should consider a backup method for your photos. You can save photos to a folder on your computer or use Google Photos, Amazon Photos (if you're a Prime customer) or invest in a backup service like Dropbox or Carbonite as examples.