Are the photos I share using the Photos app not really shared? When I share a photo to iCloud using the Photos app, subsequent edits to the photo in my library seem not so sync with the shared photo. Has sharing created a new copy of my photo?
Yes - sharing the photo puts it in a cloud backed "truth" where that image is available for all participants of the album to download and modify their copy, but not to change the original.

You'll want to share the edited version and then clean old ones until such time editing directly that shared image is implemented.