it's really really bad that we don't have an obvious word for "not secret/private, not public"... especially since that's the status of most personal/social information we have, in general and also by default.
"Discreet" is the closest word for this, and goes well with "use your discretion" which is what people are doing *always*, even if something is in fact tagged as secret (where using discretion would involve weighting that fact very strongly) or not tagged at all (where if eg a friend talked with you about their breakup you wouldn't publish the story online in their name even if nothing about secrecy was mentioned).
Ultimately whenever you tell someone you are trusting them to use their discretion, and any request for secrecy or privacy of any kind *informs* such discretion. This is why blanket requests for simply "secrecy" are way worse than specifically letting someone know why and how you want the information safeguarded. If you let them know what you're concerned about, they can collaborate with you to achieve that, rather than being bound by a sort of contract. (If you don't trust someone to not exploit knowledge of potential harms, then you're dealing with a much worse problem than someone being bad at keeping secrets, and you probably don't even want to tell them the secret in the first place!)
As I wrote in a thread above, there's a really important difference here between:
• "can't tell anyone" (can't even sensemake with allies about; must inhabit compartmentalized space as if info doesn't exist)
• "can't tell everyone" (can't publish, can't share without passing on the need for discretion, etc)
I remember a few years ago in the bay area rationality community seeing people frame untagged-but-obviously-personal information from someone else as implied private/secret (not just discreet) while _in the context of telling me the information_, which was what first tagged for me that there needs to be a clear distinction between *actually expressly secret* and discreet (tell a few people if/how it makes sense to you to do so). It seemed to me it made a lot of sense that people were sharing the things they were sharing, but there was this implicit frame that some rule/trust was sort of being broken, and that seemed really bad for actually practicing using discretion in a way that allows for continuous (rather than binary) feedback of how well it's going. Because I then sort of have to pretend to the original person who told them the information that I don't know it, otherwise I would be implying that the person who told me broke some sort of agreement. Even though I don't think any such agreement actually occurred!
So the way to do it is to clearly reserve "secret" for "do you want to hear this thing on condition of not sharing it?"—which I think is largely what Duncan is pointing at in the OP, to be clear. Makes things a lot better on this front, especially since it affords opportunities (both before and after hearing it) to explicitly request authorization for discretion moves such as wanting to talk about it with one's partner or housemates or whatever.