I think I can elaborate a little...
COMP CARD
It's sort of like a cross between a business card & a miniature version of a portfolio. It should include most if not all the basic info as stated on a business card, but should also include several photos of your work. Think one of those composite cards/leave behinds/headshots for actors/models.
BUSINESS CARD
Should include your name & position, business name & service(s) offered and basic contact information (mailing/physical address, phone number, fax number, website URL, e-mail address, etc.).
UNION CARD
A card issued by a particular Union that identifies the card holder as a valid and active member of that Union. (Sort of like a company ID).
HTH!