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sweetypie31, the important thing to remember is if you're using the Google Photos app to delete a photo, DONT TAP THE GARBAGE CAN. That will put the photo in the Trash, and that will sync across the entire Google Photos platform (i.e., anywhere you access Google Photos). You can always recover a photo in the Trash within a certain time frame (I think 30 days), but after that, it's gone.
Instead, in Google Photos, select the picture, tap Menu, then
Delete From Device. This will only delete the locally saved copy, but will leave the cloud one alone.
It's easier just to use the Free Up Space option in the Google Photos app's main menu -- this will automatically delete any of the locally saved photos that Google Photos knows has been backed up to your cloud.