With publishing you can change who can see a card within it's parent card, it is easy to spot a published card - icon of the parent will be blue!
Published cards can be seen by everyone who is a member of that parent.
Unlisted cards can only be seen by those users you have specifically added to a card. If a user joins the parent they won't be able to see this card (i.e. will not be automatically added as a member to this card). Also members of a parent who are Ghosts and Readers are only able to add unlisted cards.
A Contributor, Editor, Moderator and Author of a card are able to both 'publish' or add a as 'unlisted' to a parent. Whereas Readers are only able to add 'unlisted' cards.