&gt; I don&#x27;t agree with your use of terminology<p>When you say BST the only thing you&#x27;ve said is that it&#x27;s a binary tree structure with a property about the childrens value compared to the parent. While saying that there is certain BSTs with O(lg_2 n) searches is true, there also exists BSTs with O(n) searches.<p>The original claim was that:<p>&gt; BTW, why not BST, for everything is O(log n)?<p>Which is not true. A sorted linked list is the canonical counter example. There is no confusion of terminology, it is clearly defined in algorithmic literature on search trees.