The tarot most people picture is a specific deck published in 1909, and almost every association it carries was assigned within the previous sixty years.
Eliphas Levi, writing in France from the 1850s, made the decisive move: he connected the twenty-two trumps to the twenty-two letters of the Hebrew alphabet and so to the paths of the Kabbalistic Tree of Life. The correspondence is arithmetically neat and historically unfounded, the trumps were not twenty-two by design in the same sense, their number and order varied by city, and no fifteenth-century source connects them to Hebrew letters. Levi's scheme nevertheless became the backbone of every esoteric tarot since.
The Hermetic Order of the Golden Dawn, from 1888, systematised it: fixed attributions of trumps to letters, planets, elements and zodiac signs; the pip cards assigned to the ten sephiroth in four elemental worlds; and a decimal grid of meanings covering all fifty-six minor cards.
The Waite-Smith deck of 1909 then did the thing that made tarot usable by anyone. Pamela Colman Smith, an artist working from Arthur Edward Waite's direction and, by most assessments, contributing a great deal more than direction, drew fully illustrated scenes for the minor arcana, which older decks had shown only as arrangements of suit symbols. That single decision meant a reader could work from the picture rather than from a memorised table, and it is why this deck and its descendants dominate the English-speaking world. Smith was paid a flat fee and largely forgotten for most of a century.
Crowley's Thoth deck, painted by Lady Frieda Harris and published posthumously in 1969, is the other major line, with its own attributions and a different suit vocabulary.