A Wish Link is a page you write for one person. You choose the occasion, write what you want to say, pick how it opens, and you get a short link. Send that link however you normally talk to them.
The part that makes it different from a card is what happens next: they can answer. Depending on the occasion, that is either a straight yes or no, or a reaction and a note back. You get a private page showing whatever they sent.