Both can edit your wishlist. Full access reaches further: it can also rename the wishlist, change its settings, and delete it. A Contributor only adds and manages wishes, and only the ones they added themselves.
What each one can do
Full access covers everything a Contributor can do, plus renaming the list, changing its settings, and deleting it. It's the closest thing to a co-owner, so give it to someone you'd trust to run the list with you.
A Contributor adds wishes, and edits or removes the wishes they added. They can't rename the wishlist, change its settings, or delete it, and they can't touch a wish someone else added.
The other two levels sit at either end. Owner is you, the creator, with control over everything including who else has access. A Viewer is one invited person with read-only access: they can look at the list and reserve a gift, if you allow reservations, but change nothing. Each level includes everything the ones below it can do.
Which one to pick
Contributor for someone who should help fill the list, like a friend adding gift ideas or a partner co-planning an event, but who shouldn't be able to rename or delete it. Full access for a real co-owner who should manage the whole thing, settings included.
Not sure? Start with Contributor. You can change it later, see "How do I remove someone's access or change their permission level?"
Good to know
In the app the invite picker shows these same labels: Full Access, Contributor, Viewer.
One naming note. "Contributor" here means co-editor, not someone chipping in money. Reserving and gifting on Wishpicks never involve splitting a cost.
Access level and visibility are separate settings. Visibility says who can view the list; the access level says who can edit it. A public list can have editors and so can a private one.
Related
"What is the difference between viewing and editing access?"
"How do I invite another person to edit my wishlist?"