The are five kinds of fake difficulty, in addition to the sub-category:
Bad technical aspects make it difficult. Making a difficult jump is a real difficulty. Making a same difficult jump with overly complex controls, bad jumping physics, or an abrupt mid-air change of camera angle - and therefore the orientation of your controls - is fake difficulty.
The outcome is not reasonably determined by the player's actions. Unlocking a door by solving a color puzzle is real difficulty. Unlocking it by pressing a button until you get the right number is not.
Denial of information critical to progress. A reasonable game may require the player to use information, clues, or logic to proceed. Witholding relevant information such that the player cannot possibly win without a guide, walkthrough or trial and error is fake difficulty. Also includes hidden Unstable Equilibrium (e.g. a later level is much harder if you do badly at an early level, and you're not informed of this ahead of time). In a 2D game with no camera control, hiding important details behind foreground elements or Behind the Black counts as fake difficulty if your character should be able to see them.
The outcome of the game is influenced by decisions that were uninformed at the time and cannot be undone. (Unless the game is heavily story-based and unforeseen consequences of actions undertaken with incomplete information are legitimate plot elements, or the game offers some way of mitigating or eliminating those consequences.) A game that offers a Joke Character and is clear about the character's weakness has real difficulty. A game that disguises a joke character as a real one has fake difficulty.
The game requires the player to use skills or knowledge that are either incorrect or have nothing to do with the genre. A football game that requires you to describe the position that Jerry Rice played for a power-up is real difficulty. A football game that forces you to do multi-variable calculus in order to train your starting lineup is fake difficulty, not to mention just plain silly.