It appears to me if an album is shared privately, the person invited has to login to Adobe. However, if the album is shared publicly, no login is required. Is my assessment correct and if you know of any other nuances between public and private sharing?
Yes, if you share publicly (using the Anyone Can View setting) then anyone with the Link can view it, without an Adobe ID.
If it's shared privately (Invite Only setting), then Invitees will be required to login.
Here is the documentation:
Save, share, and invite people to contribute to your albums in Lightroom desktop
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