You’re right to point out that the difference between “not‑self” and “non‑self” / “no‑self” isn’t trivial: it reflects different interpretative choices and different emphases. In classical Buddhist scholarship, many hold that “not‑self” is more faithful to the original intent (as a via negativa) than “no‑self,” but in practice both are used. Below I’ll sketch out the nuance, show how scholars argue for one or the other, and point to key textual evidence.

The nuance: via negativa and apophatic meaning
The idea of a via negativa (negative way) is that we describe something not by asserting what it is, but by stating what it is not. So translating anatta / anātman as “not‑self” highlights that the Buddha is denying that any given phenomenon is a self (or belongs to a self), rather than asserting a metaphysical doctrine “there is no self whatsoever.”

“Not‑self” suggests a kind of functional or relational denial: “this is not mine, this is not me, this is not what I am.”

“No‑self” or “non‑self” tends to sound more absolute, more metaphysical: “there is no (everlasting) self,” or “self does not exist.” That shifts the emphasis into a doctrine of negation or annihilation, which many interpreters think is a distortion or overextension of the original teaching.

So yes: “not‑self” is more consistent with the Buddha’s own strategy of pointing out what is not self (e.g. the aggregates) and freeing one from misidentification, rather than positing a philosophical claim that “self doesn’t exist” in all senses.

Given all of that, I lean toward “not‑self” as the better translation (or at least the safer, more precise one) when aiming for fidelity to the Buddha’s mode of teaching: