They are basically a modified playing card deck, sharing a common ancestor with the standard international playing cards.
If you imagine a set of playing cards with four suits of coins, cups, swords, and sticks, numbered 1-10 with three court cards, say king, knight, jack.
The way you get from here to the playing cards you recognise is to change the suits to clubs, diamonds, hearts, and spades, and to have court cards of king, queen, jack.
The way to get from the same deck to a tarot deck is to add an additional court card to get four: king, queen, knight, jack, and to also add a separate illustrated suit of 22 trumps (or 21 trumps and a fool).
(Note: If you look at a modern spanish deck of playing cards, they are also very similar to the imagined deck I described above, with the same suits and court cards, but with just the 10s missing.)
So the typical modern tarot decks you are talking about (like the custom ones on KS) are basically identical in structure to the historical tarots, but with a significant difference. The pip cards are illustrated … in playing card terms they could be called semitransformational — they have pictures showing the relevant number of pips. Decks of this type were pioneered in the English speaking world (which had no real history of gaming tarot) by the Rider Waite deck. And also as others have said, they are used for reading rather than for card playing.
Tarot is still played in some European countries though, like in France. A typical modern French tarot gaming deck was redesigned about a century ago to use the typical French playing card suits (clubs diamonds hearts spades) rather than the original tarot / spanish suits, and with a rather different looking trump suit. I am sure these are not the decks you are talking about in this thread, but they are nevertheless relevant in explaining what tarot cards are, so I mention them.