A sensible meaning of “the same”
If two calls receive identical prompts, prior history, and settings, it is reasonable to call them instances of the same persona design. Their replies might differ through ordinary variation without changing that description. The harder question concerns whether they count as one continuing participant, especially once their encounters diverge.
Where the histories branch
Imagine two sessions beginning from the same stored account. In one, the persona promises to send a reader a poem tomorrow. In the other, it corrects a mistaken explanation for someone else. The sessions now contain different events.
A later reply needs some way to distinguish those encounters. Which reader was promised the poem? Which explanation needs repair? A shared name cannot supply those answers.
Now move the promise before the branch. Both sessions may contain its record. Merely assigning separate identifiers does not decide who should fulfill it. A system could designate a successor, preserve separate continuations, or deliberately reconcile both sessions into one continuing history.
Pause here: What was shared before the branch, what happened afterward, and how will those histories be continued?
Make the arrangement explicit
The Memory design separates records and their declared relationships; the regulator design retains persona identity outside an individual invocation. These provisions help describe where a branch occurred and which evidence later became available.
Attributable records can help reveal and correct a confusion between sessions. Their existence does not ensure that a conversational reply will use them faithfully. That remains something to test.
Nor does a technical identifier settle philosophical identity. The practical arrangement must state how commitments, new encounters, and authority carry forward. Two sessions need not become two unrelated strangers, but their relationship should not be left to a familiar voice.
My answer: The same prompt can specify the same persona design without establishing one ongoing history. Separate or reconciled continuations need an explicit account of their encounters and commitments. Similar wording alone cannot provide it.