There are three game modes that an Adventure in AI Dungeon can have: Creative, Adventure, and Hardcore.
Creative Mode is the default mode; All commands are enabled, and you can freely revert and alter the AI's output. This particular gamemode is usually best for long stories, and when you wish to take greater control over the AI's outputs.
Creative mode is also recommended for newcomers, or those wishing to use AI Dungeon for AI-assisted creative writing. Alter and Story are powerful tools to use, not to mention Revert and Redo.
Adventure Mode is the second gamemode currently available, and is intended to add an additional level of challenge, while still allowing you to get out of a bad situation with Retry and Undo. However, it removes the Alter command and Story input mode to challenge your writing style and make AI Dungeon feel more "game-like."
Adventure mode is usually the mode of choice for playing special Challenges issued by other players.
Hardcore Mode is an Adventure Mode in which you cannot use Undo, Alter, Remember, Retry, or the Story input mode. It also contains a script that ends the game permanently when it detects the death of "you".
Hardcore Mode is not recommended for anything but specific challenges, and should especially not be used if you want a long or coherent story.
Hardcore mode is usually used by creators to instill a sense of realism within their scenarios. Because of this, the drawback is that a long and coherent story is not possible as aforementioned. For newcomers, this is a mode that is not recommended to start off with, as it requires a bit of experience and time playing with the AI.