In MTG Arena, card sleeves are cosmetic upgrades that change the way the back of your cards look. These stylish improvements can be applied from the deck builder page by clicking on the deck box and then selecting which card back you'd like to use from the ones you have available. Once acquired, a card sleeve can be applied to any deck in your collection. You can choose the card sleeve to apply on a deck-by-deck basis; you can have different card sleeves for every deck if you so desire! Applying a card sleeve is optional. You'll be able to swap between card sleeves and the default card back in the deck builder.
Card styles, on the other hand, allow you to change the way the front of your cards look in MTG Arena. You'll be able to see which cards have card styles in-game through the deck builder, which has a filter option specifically for card styles. Selecting a card will also provide more information on how the card style can be obtained. Card styles do not add card/s to your collection. Once acquired, a card style can be applied to all cards with that illustration—you don't need to acquire it more than once. Card styles are based on the card's illustration. This means that if a card shares an illustration across sets, once you've unlocked the card style, it will apply to any card in your collection with that illustration. If the card appears in a set using a different, it will have a separate card style you can acquire.
It is possible to acquire card styles for cards you do not have in your collection. If this happens, you will be able to apply the style once you have the card in your collection (you won't have to re-acquire the style). Applying a card style is optional. While the option is enabled by default, you will be able to swap between using card styles and the default illustration in the deck builder.