There is some crossover. Both IF and ARGs (Alternate/Augmented Reality Games) are interactive in some similar and different ways.
IF is usually played by a single player who is interacting with a single complete story file (usually in a browser or via download in some type of engine or interpreter). They know they’re reading a story even if they are immersively role-playing a character.
The main difference with an ARG is the story in some way “spills out” of the normal expected narrative boundaries of traditional media into an alternate fictional “reality” with plot elements or extra lore to be found in the “real world” - or more specifically the game’s “alternate reality”.
Many historical ARGs are quasi-multiplayer, and frequently might not have an obvious entry point. Players often stumble upon the game with an odd link hidden on a website, or by noticing that certain numbers on a movie poster are highlighted which when put together form a phone number they can dial, which might in turn feed the caller a clue where to explore next. The entry point might be a single frame of an online video with a URL that leads to another “hidden” video that many people don’t notice or information may be hidden in HTML site data normal people would never run across. Often the idea is this “alternate reality” is intruding upon the player, often taking the guise of a hidden conspiracy or scavenger hunt. Players might need to research websites that appear real and might need to “hack in” by obtaining a login and password of a fictional character elsewhere. There may be real-world geocaches involved, phone numbers to call, or even a prize someone can find in an actual location.
An ARG often might include improvisation by the game runners with player interaction, where a player might send an email to an in-game character where it may be actually answered, or they might even be sent a physical artifact or clue. Often communities develop to interpret these clues in cooperation and players may actually find their persona worked into the narrative.
ARGs often end after a period of time once the game is communally “solved”.
Examples of ARGs:
Back in the late 90s there was a short-lived commercial game called Majestic where players signed up and agreed to receive potentially menacing phone calls or faxes with clues or characters warning them not to keep researching a potentially dangerous conspiracy theory.
The movie The Blair Witch Project had a viral marketing campaign which initially was designed with the fiction that the movie was real found-footage and the characters had actually disappeared, and there were hidden websites where the curious could research backstory and secrets.
I Love Bees - a game run by the devs of Halo as viral marketing and backstory for a new game.
Marble Hornets was a stealth YouTube series that started as innocuous guys posting workout videos, but contained terrifying images of Slenderman in the background and became an entire online web series, which included viewers who were able to post and interact with the characters, and some received clues and artifacts sent by the show runners.
YouTuber Night Mind calls these “UnFiction” where a series of videos include clues and rabbit-holes revealing more backstory, and ergodic elements for the audience to find even if it’s not a formal game. Unfiction is sometimes also an alternate moniker for ARGs - usually that involve hidden searchable lore without an extensive game element.
IF, while not strictly an ARG, may include ARG elements such as the recent Wikipedia-esque Excalibur.