For example, Borderlands uses ECHO logs, there are audio entries in BioShock, RPGs often have "books" that you can collect pages to read a mini bonus story.
Is there a term more specific than "collectible" which conveys the element of storytelling?
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In general, when these are not necessarily collectibles, they’re called the environmental storytelling.
Specifically for collectibles, I have seen “narrative collectibles” used here and there. Other options may include: narrative objects, collectible narrative objects, story collectibles.
If you're looking for a more general term, Tynan Sylvester refers to details which provide flavor but don't directly impact the main gameplay as "Hair Complexity."
Hair complexity is my term for pieces of the simulation that don’t affect anything outside themselves.
I call it hair complexity because it sticks off the main ball of relationships without feeding back into it, like the hair on your head. Such hair complexity can be ignored by players who don’t wish to deal with it, while more interested or skilled players can pay attention and get its full flavor. It’s like the flavortext in a card game.
Source: The Simulation Dream