The event's shared link has no name on it, so before answering, a guest says who they are: a first name, and a mobile or an email.
With public replies off, the mobile or email has to be the one you have for them; the line under the field says so. Their answer then lands on their own row, the same as if they had used their own link, and counts once. If you have no mobile or email for them, their first name finds their row, as long as only one person on the list without contact details has that name; what they typed is saved on the row.
If what they type isn't on your list, they are told so and nothing is saved. They can try another, or ask you for their link.
With public replies on, someone not on your list joins: they get a row on the event and a place in your People, and their answer counts. Someone who is already on your list is matched by their mobile or email and answers on their own row.
Matching is exact. If you have someone's email and they type their mobile, they won't match: with public replies on they join as a second row, and with them off they are refused.