So, you're both partially right. There was a 4-issue miniseries in 1991 and each issue had a trading card-sized hologram on the cover. The holograms were sort of built into the cover and not really removable. Someone could cut them out and have a "card" if they wanted. Each issue had variant cover illustrations but always had the same hologram, (ie. issue #1 always had the Robin hologram). Also, each issue had one variant cover version with no hologram card.
The cards in this checklist were packaged as actual separate trading cards and the hologram images are the same as the holograms on the comic covers. You could get one card in a Collector's Set that included all variant covers of a particular issue plus the corresponding hologram trading card. Additionally there was a Deluxe Collector's Set which contained all four comics and their variant covers, (14 comics total), as well as all four trading cards.
Robin II: The Joker's Wild! [Comicvine]
(The above site has links to each issue and images of all covers.)
ebay listing: ROBIN II DELUXE Collector's Set includes 4 issues & hologram cards DC 1991 NEW!
(Bad listing title. Not actually the Deluxe set.)
ebay listing: Robin II Deluxe Collector's Set Sealed 1991 14 Comics 4 Trading Cards More