I think strictly speaking that the cards described in Turtle Recall
are the entire deck of the Caroc which is the Disc equivalent of Tarot (and features more in Light Fantastic when Twoflower falls into a coma after rescuing Bethany from the Druids?) and so the 'new' suit is in fact what would be equivalent to the major arcana or trump cards, whilst the cards for CMO appear to be played using the minor arcana/suits which here on Roundworld are the ones that make up a traditional game-playing deck with the major cards left mainly for fortune-telling purposes.
Swords, Cups, Coins/Pentacles/Discs and Staves/Wands were the original suits for tarot and card games, but in late medieval France and thence to England they were changed to Hearts (Cups), Diamonds (Coins), Clubs (Staves) and Spades (Swords) possibly because the symbols were so poorly printed, or else to move away from the 'witchery' reputation of the Tarot in the christian world although that's rather odd since Italy and Spain both stayed with the minor arcana symbology - go figure!
Just to complicate things Germanic areas (including Switzerland) use Roses or Hearts, Bells, Acorns and Leaves or Shields and of course there are other variations all over the world, although the traditional Spades, Diamonds etc is mainly used in most English-speaking countries