if I delete an old backup, will the photos from that backup be deleted off my Mac?

No, if you delete a backup then you cannot restore that backup in future. Deleting a backup has no impact on what is currently on the device, stored in Photo Stream, iCloud Photo Library, or a Photos library. My point is that you would be wise not to rely on just one copy for anything that matters to you. A Photos library is a complex container. If something goes wrong with it then you may have trouble pulling out the images. I make a point of copying off my images to a set of folders split by year and month which I then add into Photos. Both my original images and my Photos library are then captured in Time Machine. If I make a mistake or a piece of hardware fails I shouldn't lose anything.

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