Why might the deck matter when you receive a reading? Obligatory disclaimer, just this once: everyone reads tarot differently and there's no single correct way. We'll stay in the Western hermetic mystery tradition and look only at the minor arcana, using the Seven of Cups across several decks to show how each one layers in more information.
Marseille: read the number
In the Tarot de Marseille the pips are unillustrated, so you read the number. In the Qabalistic system, seven is Netzach — instinct, nature. So if the Seven of Cups turns up in a situation, I might say: go with your instinct, you're a natural for this. Sevens are of nature — the seven colors of the rainbow, the seven classical planets, the seven days of the week. That numerology is the system that branched its way into Freemasonry, and you'll find the same approach in Masonic decks like Brother Patricio Díaz Silva's Masonic Tarot: still just "seven," read off the Qabalistic numerology.
Rider-Waite-Smith: add the element
Arthur Edward Waite — a Freemason, later a member of the Golden Dawn — partnered with Pamela Colman Smith, whom he hired to illustrate the deck now often called Waite-Smith. Here the numerology is still present (seven is still that natural, instinctual number), but the cups now carry the hermetic element of water: heart, flow, emotion, intuition, a receptive energy. So it's not just natural — it's natural of the heart. And seven follows the harmony of the six and precedes the power of the eight, so when the heart is in its natural place, what does it do? It dreams, it aspires, it imagines. That's the Seven of Cups. Waite is sometimes said to have held back secrets in this deck — but it's by far my favorite to read, and the cornerstone of a baseline reading.
Golden Dawn decks: add the planet
For the "withheld secrets," look to Godfrey Dowson's Hermetic Tarot, which rolls in another layer: planetary correspondence. The Seven of Cups is Venus in Scorpio (fixed water). Venus doesn't express well in Scorpio — not in fall, but not in its domicile or exaltation either. Venus wants to harmonize and see beauty; Scorpio wants to transform and hides its passion. So the dreaming gains a restless edge: a life that isn't quite harmonized, an enjoyment shadowed by a hidden pull to break out and transform. Same card, different explanation. (I don't actually read with the Hermetic Tarot much — honestly, the black-and-white art isn't enjoyable to look at.)
Chic Cicero's Golden Dawn Ritual Tarot (with Sandra Tabatha Cicero) takes it a step further, adding color-coding — the blue of water, the green of Netzach — to lock the interpretation into the Qabalistic frame rather than drifting into other numerology systems. With this deck I don't use upside-down reversals at all; instead I read by the elements of adjacent cards. If the card signifying "me" is the Seven of Cups and the card before me is a stable wands card, I read them somewhat like a reversal, because those elemental energies aren't suited to one another. So I use particular spreads with this deck precisely because I'm looking at how things interact, not just at single upright or reversed cards.
A note on reversals generally: in the Rider-Waite system I read a reversed card as blocked energy, or as not perceiving a situation properly — not as the opposite energy. There's already a card in the deck that defines the opposite, and it would be just as likely to come up.
The decks I collect but don't read with
There are far more decks out there. I collect several for their beauty — the Rosa Mundi among them — but don't read with them. I've read through the Book of Thoth and used the Thoth deck in a few readings while apprenticing under Cliff, but it just doesn't fit my energy; it's almost like heavily dialected English I half-understand, and it doesn't flow for me. I also have plenty of others — Zelda and Dungeons & Dragons decks, and at least four other Golden Dawn decks, including Israel Regardie and Robert Wang's, which is color-coded and a fun mix of the styles above. And of course many people read from a New Age perspective — psychic ability, holy guardian angels, ancestors, summoning the card's magic. I don't claim one is better than another; they're just completely different things.
The point is simply this: there are reasons your reader is using the deck they're using. Next time, I'll do the major arcana breakdown the same way.