Algorithmic difficulty is the design and placement of game content to correspond to an escalating 'difficulty level' in the game: either by generating content to correspond to a difficulty level, or by assigning a difficulty level to already generated content.
This is typically seen in Diablo style RPGs and some roguelikes which use instancing of in-game entities to create randomized items. Less frequently it can be used to determine the relative difficulty of hand-designed content to be subsequently placed procedurally, as can be seen with the monster design in Unangband. For example, the designer can rapidly create content, but leaves it up to the game to determine how challenging that content is to overcome, and consequently where in the procedurally generated environment this content will appear. Notably the Touhou series of bullet hell shooters uses algorithmic difficulty. Though the users are only allowed to choose certain difficulty values, several community mods enable ramping the difficulty beyond the offered values.
Algorithmic difficulty can either attempt to estimate relative power based on the combination of content attributes (ontogenetic) or simulate an idealized player encountering or using the content to determine it's relative effectiveness (teleological).
What distinguishes algorithmic difficulty from adaptive difficulty is that the difficulty level remains fixed in the game and does not adapt to player actions: usually by having different geographical zones correspond to different difficulty levels. This still allows the player to 'adapt' to differing difficulty by moving between geographic zones, but only in the sense that switching the game off allows the player to adapt to an abrupt difficulty spike.
