Cards: Each card belongs to a different collection, collect them opening card packs.
Albums: An album belongs to a collection, collect all cards in an album to earn collection coins.
Packs: Each pack belongs to a collection, open cardpacks to collect cards. You can find card packs as rewards in different parts of the game.
The Card Packs that you win will be locked to a specific collection so its better to open them right away to help complete your current collection. If you have any unopened packs in your inbox once the collection is over, they will not work for other collections.
Coins: To collect new tiles you will need to spend coins, you can get coins by completing albums and with repeated cards.