They are both preset decks
In the Deck of Many Things there are nine cards which are marked as only existing in the deck when there are all twenty-two cards, thus there are thirteen cards left and these are what make up the thirteen card deck, namely every King, Queen, and Jack and also the Joker (without TM):
- Ace of diamonds Vizier*
- King of diamonds Sun
- Queen of diamonds Moon
- Jack of diamonds Star
- Two of diamonds Comet*
- Ace of hearts The Fates*
- King of hearts Throne
- Queen of hearts Key
- Jack of hearts Knight
- Two of hearts Gem*
- Ace of clubs Talons*
- King of clubs The Void
- Queen of clubs Flames
- Jack of clubs Skull
- Two of clubs Idiot*
- Ace of spades Donjon*
- King of spades Ruin
- Queen of spades Euryale
- Jack of spades Rogue
- Two of spades Balance*
- Joker (with TM) Fool*
- Joker (without TM) Jester
*Found only in a deck with twenty-two cards