When a chest says it has 10 cards, it can give up to 10 units of the same card, or 10 units split into different cards. The amount of different card types in a chest depends on the chest type and its Castle.
The description of "Contains at least" refers to the total amount of cards rather than the variety of cards within its rarity. You can check how many cards of each character you received by verifying the number written on the cards as soon as you open the chest. If you read "x20", for example, it means you receive 20 cards of that type.