good question. While the <button> tag can be used for links, that's not its technical purpose. They're designed for use with forms.
An <a> takes you somewhere, while a <button> performs an action. Screen readers will also read links as links and buttons as buttons, the latter inferring action.
So a "button" in the context of my article refers to links that have the visual appearance of buttons.
More:
https://www.w3.org/TR/2011/WD-html5-20110525/the-button-element.html