There's two seperate decks. There's the Collectable Cards, aka the NeoDeck, those are the ones that just have names (usually characters) and a picture, and show up on your profile (https://www.neopets.com/games/neodeck/index.phtml?owner=col_mack). Think of them like baseball cards! They have a hiscore table, but otherwise serve no function.
And then there's the TCG deck, or the Trading Card Game, which are the ones that are based on the old IRL game deck, that have rules for a game similar to Magic the Gathering or YuGiOh, which are collected here: https://www.neopets.com/tcg/album.phtml and I guess at one point you could play matches on the site? That looks like it's gone now, though.