An AI story generator takes your prompt, your characters or your preferences, and writes fiction from them. In this niche they range from a single generated story to open-ended adventures where you steer every turn, and some of them also narrate the result aloud.
What you are actually buying
Three things, and they are priced separately almost everywhere. Generations, meaning how much text you can produce. Context, meaning how much of the story the model can still see, which is what decides whether it remembers a character introduced an hour ago. And memory, meaning explicit notes the service keeps between sessions.
Tiers are usually sold on context size, which is why the same service offers plans that look identical until you read what each one holds in its head.
Why the content rules differ so much
Because the rules belong to whoever supplies the model. A service running its own model can allow what it likes; one built on somebody else's API inherits that provider's restrictions, and a tool that lets you bring your own key passes the question to you. This is why two apps that look identical can behave completely differently on explicit prompts.
The useful question is never "is it uncensored" but "whose model is it, and what does that provider forbid". Where a service publishes the answer, it is worth more than any marketing claim about freedom.
Generated libraries
Some apps are not generators at all: they publish libraries of stories a model wrote in advance. The store listing sometimes admits this and sometimes does not, and it is a fair thing to want to know before paying, because an AI-written library is a different product from one with authors behind it.
See also interactive fiction and the glossary.