My point of view origins from the academic world, and the distinction absolutely matters, and it should matter in any theoretical discussion  on the topic, otherwise we&#x27;ll spend too much time arguing semantics, instead of just being clear.<p>&gt; not strictly all self-balancing BSTs have all O(log n) operations.<p>You&#x27;re right. You could have a self balancing tree that would simply guarantee it&#x27;s height is n&#x2F;2, but that entails that it&#x27;s height is O(n), which, by most definitions mean that it&#x27;s not self balancing. You want it to be at least O(n^c) for 0&lt;c&lt;1, in height.