Thoth Tarot, Knights, Kings...

[Celtaur]

The High Court cards in the Minor Arcana are named different with the Thoth tarot than most traditional decks.

Traditionally we see the Page, Knight, Queen, Kings as the ascending ruling hierarchy.

In the Thoth deck we have a different set being the Princess (Page), Prince (Knight), Queen (Queen) and Knight (King).

The change of the Knight with the King and the Prince with the Knight has me curious. Why?

[Haruth]

Simply because the attributes sit better with the alchemical symbolism, Celtaur.

The Knights are the most sublime, original, active part of the Energy of the Element. Their action is swift and violent, but transient. In the element of Fire, e.g. the Knight corresponds to the Lightning flash.
...
The Queens are the complements to the Knights. They receive, ferment, and transmit the original Energy of their Knight. Quick to receive that Energy, they are also fitted to endure for the period of their function; but they are not the final product. They represent the second stage in the process whose fourth and last stage is material realisation.

The Prince is the Son of the Queen (The old King's daughter) by the Knight who won her: he is represented therefore as in a chariot, going forth to carry out the combined Energy of his parents. He is the active issue of their union, and it's manifestation. His action is consequently more enduring than that of his forebears.

The Princess represents the ultimate issue of the original Energy in its completion, its crystallisation, its materialisation. They also represent the counterbalancing, the reabsorption of Energy.

No sooner has the Princess made her appearance than the Prince wins her in marriage, and she is set upon the throne of her Mother. She thus awakens the Old King, who therupon becomes a young Knight, and so renews the cycle. The Princess is not only the perfect Maiden, but owing to the death of the Prince (concurrent with the appearance of the Princess), the forsaken and lamenting Widow.

Book of Thoth

In particular, the final paragraph is an allusion to the central alchemical process.

Crowley further refined the alchemical attributes applied to the tarot generally, by identifying each of the court cards with an element. Thus are identified:

Knights with Fire
Queens with Water
Princes with Air
Princesses with Earth

Such complex alchemical principles as Fire of Fire, Water of Fire, Air of Fire, and Earth of Fire can therefore be expressed under the Crowley system.