Since you’re being abstruse, consider information by definition is in possession by an entity (or rephrased a property of a system). For that information to move the system needs to be brought into contact with another system, and it is the nature of this contact that is being policed. If information doesn’t have an ambient system that is discernible then there is no distinction to be made if its sensitivity—it may as well be noise.
In practice, "organization" usually means your company or business. "The community" usually means an Information Sharing and Analysis Center (ISAC) aka a group of similar orgs that share information with each other; think financial services companies in the US, or energy companies in Japan.
Okay, maybe I'm just not the target audience for this. I didn't know what an ISAC was, but I've seen plenty of TLP markers on open source disclosures where it was exceedingly unclear what a "community" meant w/r/t appropriate sharing.
If you see something publicly it's TLP:White (or clear, since it was changed for weird readons) by definition. But yeah it's a term specific to it security, where it's usually well understood what TLP:Amber and TLP:Red means. I agree TLP:Green is a bit more fuzzy, and the intention is often basically "share with trusted parties but don't post publicly".