What's the difference between three of cups and three cups?
Solution 1:
Cups is a suit in the Tarot deck. The three of cups is a particular card in the tarot deck - the third card in the suit of cups.
The Three of Holy Treasures could be a reference to a non-traditional tarot deck - there are thousands of variations of decks - see facade.com for reference. In that case, 'Holy Treasures' would be the name of a suit in such a different deck, and we would be talking about the third card in that suit.
People make up all kinds of suit names and card names and publish their own tarot decks, the suits and cards can have all kinds of different mames, like stars, globes, holy treasures, planets, rainbows - whatever!
The classic tarot deck is referred to as 'Rider-Waite' and was published in 1910. Have a look if you are interested in finding out the 'classic' tarot suit names.
Three cups would just mean three cups - like 'three cups sat on the shelf'. Three treasures would mean just three treasures - 'the wise men brought three treasures to Jesus'. This would be nothing to do with tarot - just talking about regular items.
If you were playing normal cards you could say 'three clubs' meaning any three cards from the suit of clubs. Like 'the man was dealt three clubs'. This would normally be in the context of the cards you hold in your hand. This is less likely in tarot - these days, tarot cards are laid on the table in a spread - a planned out arrangement - not dealt in 'hands'.
Hope that helps!
Solution 2:
There's a significant different between the two, and they are not interchangeable.
The phrase "three of cups" is used specifically in the context of tarot cards, where "cups" is a suit, in the same way that clubs is a suit in a deck of normal playing cards. It's the same expression as "the five of diamonds". Outside of this usage, I can't think of any other meanings the phrase could possibly have.
You might say something like "three of the cups", however. For instance, if there were ten cups on a supermarket shelf, and someone asked how many of them you were going to buy, you could say "I'm going to buy three of the cups". But saying "I'm going to buy three of cups" would be incorrect. Interestingly, you could say "I'm going to buy three of them", which is a similar but distinct version of the phrase.