Ok setting all of Joe's settings, and I already seeing new activity (it's bringing back old deleted shots into my laptop I don't want!)
Those old deleted shots were/are hanging around somewhere in the system, maybe on iCloud, or I am betting on your iPhone, but they were/are obviously somewhere where they had not been deleted. They are showing up again/now because all of your systems are getting into synch via the iCloud Library.
My suggestion would be to use Photos on either your Desktop or your Laptop and delete them (it is much easier to select and delete groups of images on MacOS than it is on iOS or iCloud.) Because your Libraries are all synched (in fact mirror the iCloud Library) deleting them on either MacOS device will delete those unwanted images from iCloud and therefore from all your devices. With is what you want.
AN OBSERVATION: When you drag an image from Photos to say your desktop on your MacOS devices, if you watch the image icon title closely you may notice the size and resolution of the image will increase over a period of a few seconds. This is because the image in Photos is "
optimized" for viewing on your Desktop/Laptop screen and there is a slight lag while the full resolution and size image is quickly downloaded from Photos on iCloud. (I hadn't observed/noticed this until I was experimenting to be sure of my facts in this thread — thanks for filling in that blank.
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