No, there's not distinction here that actually matters to RPGs. There's nothing inherent to the fiction imagined, but rather the process -- the authorities and constraints -- that make the difference. IE, there's no difference between me imagining a culture or murderer and you doing the same. The only bit that makes either of these imaginings useful to an RPG is which of use has the authority to have our imagining enter the shared fiction. And what constraints we're under for what we can enter into the shared fiction.
To expand this a bit, the only difference between the player imagining who killed the Duke and the GM imagining who killed the Duke is who gets the say to make their version the one that's entered into the shared fiction. The GM imagining the murderer is not some special or different process, or privileged in any way, over the player except for those authorities. The same applies to cultural details. And, between imagining murderers or cultures, there's again little difference because anyone can imagine anything at any time. It's what constraints that apply that matter -- is it the proper time in game to author a murderer or a culture?
And, once we realize that it's actually the authorities and constraints that matter, it makes it much easier to look at a different structure and walk through the process of play and how it differs.
I had hoped a different statement of it might help, as this is one of the points that's been made repeatedly and seems to not be landing.