Interactive fiction is writing that asks the reader to do something: choose, type, explore. The term dates from text adventures, where you typed instructions and the program answered in prose, and it has since widened to cover anything that gives the reader a say in what happens next.
The three shapes it takes
Parser fiction is the original: you type what you want to do. It is still written and still has a devoted audience, and it is the least common shape in adult writing, because typing breaks the mood for most readers.
Choice fiction gives you options to pick from. This is what almost every adult story app means by interactive, and it is the easiest to write at volume.
Hypertext links passages together and lets you wander. It sits behind a lot of free browser erotica, often built in tools made for exactly this and hosted by the author.
Interactive fiction and interactive erotica
"Interactive erotica" is the commercial label and usually means choice fiction with explicit scenes. The difference is not technical. Interactive fiction describes a form, interactive erotica describes a product, and the second one is what an app store listing is selling.
Why the distinction is worth keeping
Because the amount of real interaction varies enormously, and the word hides that. A story where your choices change who you end up with is a different thing from a story where the choice costs coins and alters one line of dialogue. The useful questions are how many endings exist, whether choices are remembered later, and whether the app says so anywhere.
Where it lives
Two worlds, barely overlapping. The hobbyist one is free, hosted by authors and competitions, and is where the formally adventurous work happens, including most of the explicit writing that experiments with form. The commercial one is the app stores, where the format is standardised and the money is in premium choices. A reader who only knows one of them is missing most of what exists.
See also branching story, choice-based story and the glossary.