Every wishlist can be shared, so there's no separate "shared wishlist" type to create. Make one as usual, then pick how you share it. Send the link and people can view it. Invite them by email and they can edit it with you.
Those two are genuinely different. A link lets anyone who has it open the list and look at it, and reserve gifts if you allow that, with no account and no invite. An email invite is real co-managing: you name a specific person and give them an access level, so they can add and change wishes.
Steps
Create a wishlist the way you normally would and add a few wishes.
To let people view it, open the wishlist and copy the share link, then send it however you like. New wishlists start as Anyone with the link, so anyone you send it to can open it.
To let someone edit it, open the wishlist's access settings, type their email address, choose Contributor (add and manage wishes) or Full Access (also change settings), and send the invite.
They accept the invite, sign in with that same email, and can start editing.
Good to know
You don't need to make a wishlist private before adding editors. Who can view and who can edit are two separate settings, so a list you've shared by link can still have editors.
A plain link never grants editing, only viewing and reserving. Editing always comes from an email invite plus an access level the person has accepted.
Related
"How do I invite another person to edit my wishlist?"
"What is the difference between viewing and editing access?"
"Can several people manage one wishlist together?"