There are three types of cards in Pet Master, all which make up pieces of the different sets and albums.
Common cards, denoted by their white border, are the easiest to find and make up the large bulk of each card set. These cards can be found in every chest in the game and can also be freely traded with friends to help each other complete sets.
Gold cards can be identified by their gold border and are much more rare than common cards. These cards can more commonly be found in the Owl and Lion chests. Gold cards can be traded as well, but only during very special events.
Royal cards are the rarest of the different card types and can only be found in royal chests and as rewards in some events. These can be identified by the royal badge found on the top left corner of the card.