The answer to "how many difficulties" is a nine-step staircase with no ceiling. Sad Socket published the ladder in the official Patch #17 notes, and unlike most roguelike menus, the titles are the joke and the system at once: you climb the feudal ladder from Peasant to King, and then you keep climbing through numbered crowns.

The official ladder
| # | Title | Official description |
|---|---|---|
| 1 | Peasant | Chill |
| 2 | Squire | Very easy |
| 3 | Knight | Easy |
| 4 | Lord | Medium-easy |
| 5 | Baron | Medium |
| 6 | Count | Medium-hard |
| 7 | Duke | Kinda hard |
| 8 | Prince | Pretty hard |
| 9 | King | Hard |
| 10+ | King II and on | Very hard |
| Deep end | King IX and on | Possibly unwinnable |
That last row is quoted from the patch notes, typo included: the official text reads "Kng IX I and on: POSSIBLY UNWINNABLE". We kept the typo in our transcription for the pleasure of it; the meaning is clear. The numbered crowns go up indefinitely, which is the developer's way of saying the ceiling is whatever your seed and your sanity allow.
How the ladder interacts with everything else
Clearing a difficulty stamps everything below it. Beat King, and every lower title shows as cleared too, which matters for the achievements that count completions. Experience scales with the title, adjusted in patches to roughly 10 to 20 percent differences between steps, so higher play levels your kings faster. And clearing any difficulty at King or above triggers the King of Kings achievement, one of the game's marquee unlocks.
The difficulty titles are also separate from the quest mode's three settings (Knight, King and Chaos), which modify the 81-challenge world map rather than the main runs. Do not confuse clearing the King difficulty with beating the King-tier quest challenges; they are different systems.
What does "max level" mean here?
The search-friendly phrase "max level" means different things in this game, so here is the whole picture. Cards and plots cap at level 3 normally, with your base's cap extendable through perks and the Progress king's Futurism decree letting troops reach level 99. Your king's own level, the one that earns perks, keeps rising as long as the run does; the community has documented kings past level 30 with the perk screen still showing locked slots, and the developers have not published a hard cap.
FAQ
How many difficulties are in 9 Kings?
Nine base difficulties, from Peasant to King, per the official Patch #17 notes. Above King, the tiers continue indefinitely as King II, King III and beyond.
What is the highest difficulty in 9 Kings?
There is no highest one. The ladder continues through numbered King titles; the patch notes describe King IX and above as possibly unwinnable, which is as close to a ceiling as the game gets.
What difficulty should you start on?
Peasant or Squire if the genre is new to you; Knight if you have played auto-battlers before. The early titles are genuinely tuned as on-ramps, and clearing them stamps up the ladder.