Just a quirk of history, I believe. Consider how any new idea - a sport, a game, a technology - gets exchanged between different countries. In the early days, not only do the early adopters need to import the equipment needed (such as packs of cards) but they also need new words, often borrowed from other languages, for descriptions and concepts. As with board-games now (“meeples”, “worker placement”, “engine building”, etc.) so it was with playing cards in 15th century England.
The other thing to remember is that it can take a while for both designs and terminology to standardise.
So now imagine a group of friends in Elizabethan England settling down for a games night. One of them brings along the set of cards. This particular set has been imported from France (and hence has the same French design of suits that we are familiar with today). But Italian-designed sets of cards were also in common use. As the evening progresses, one player might teach his companions a card games he knows – which might involve referring to the names of suits as he knows them. So it is that he might point to a French card (showing the trefoil/clover design) but be thinking of the equivalent Italian suit. And we can deduce that the player is picturing the Italian card but doesn’t know the Italian word for it (bastoni, meaning baton) because the word that “sticks” in English for this suit is “club” (meaning a stick).
There’s a similar story with the suit known in English as spades. I don’t think the French design (described as pikes in French and leaves in German) looks much like a spade. But the equivalent suit in Italian cards shows a sword, so at some point the Italian word for sword (spade) has been applied to the French design.