The four tarot suits are older than tarot. They arrived in Europe already assembled, on ordinary playing cards, and the trumps that make a pack a tarot pack were added to them afterwards.
The suit that changed its object
A surviving Mamluk pack held in the Topkapi Palace collection in Istanbul carries four suits: cups, coins, swords and polo-sticks. The first three passed into the European Latin suits unaltered. The fourth did not, because polo was not played in the places the cards reached, and the long-handled implement became a baton, a staff or a club. The suit this atlas calls Wands is that one.
That substitution is the clearest single piece of evidence for the transmission route, because it is the kind of change that happens when an object is copied by people who do not recognise what it depicts.
Fire, or air
The elemental attribution of this suit is genuinely contested. The system set out by the Hermetic Order of the Golden Dawn in the late nineteenth century assigns Wands to Fire and Swords to Air, and that assignment is the one most decks and most modern books follow. Other occult writers reverse the pair, giving Wands to Air and Swords to Fire, and the reversal has never entirely gone away.
Neither assignment is old. The suits reached Europe with no elemental scheme attached, and every version of the correspondence dates from the eighteenth century or later.
Sources The Game of Tarot: From Ferrara to Salt Lake CityMichael Dummett with A Wicked Pack of Cards: The Origins of the Occult TarotRonald Decker, Thierry Depaulis and Michael Dummett