Viewing means someone can look at your wishlist and reserve a gift. Editing means they can add and change the wishes. Viewing usually works straight from a shared link with no account, while editing takes an email invite and an access level.
The access levels
Owner is you, the person who created the wishlist. You control everything on it, including who else has access.
Full Access does everything a Contributor does, plus renaming the list, changing its settings, and deleting it. Closest thing to a co-owner.
Contributor adds, edits, and manages wishes, but can't rename or delete the list, and can only change the wishes they added.
Viewer is read-only for one invited person. They can look at the list and reserve a gift, if you allow reservations, but change nothing.
When you invite someone, the picker offers Full Access, Contributor, and Viewer. Owner is just you.
Anyone you simply send the link to gets the same read-only experience as a Viewer: they can look and reserve, not edit.
Good to know
Edit access doesn't depend on visibility. A wishlist shared by link can have invited editors, and so can a private one. Visibility decides who can view, the access level decides who can edit. A Viewer never edits, however the list is shared. If you want someone to change wishes, invite them as Contributor or Full Access.
Reserving a gift isn't editing. It doesn't change what's on the wishlist. See "How does gift reservation work?"
Related
"How do I invite another person to edit my wishlist?"
"Why can't someone edit my wishlist?"