There's no separate "shared wishlist" type — every wishlist can be shared. Create a wishlist as normal, then decide how to share it: send the link so people can view it, or invite people by email so they can edit it with you.
The two kinds of sharing work differently. Sharing to view means anyone with the link can open the wishlist and look at it — and reserve gifts, if you allow it — with no account or invite needed. Sharing to edit is real co-managing: you invite specific people by email and give them an access level so they can add and change wishes.
Steps
Create a wishlist as you normally would and add a few wishes.
To let people view it, open the wishlist and use the share option to copy the link, then send it however you like. New wishlists start as Anyone with the link, so anyone with that link can open it.
To let someone edit it with you, open the wishlist's access settings, enter their email address, choose an access level (Contributor to add and manage wishes, or Full Access to 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 do not need to make a wishlist private to add editors. Visibility (who can view) and access level (who can edit) are separate things — a list shared by link can still have editors.
A plain link only lets people view and reserve, never edit. Editing always requires an email invite plus an accepted access level.
For the exact invite steps and access levels, see "How do I invite another person to edit my wishlist?" and "What is the difference between viewing and editing access?" And if you want a whole group involved, several people can co-manage one wishlist — see "Can several people manage one wishlist together?"