Object Oriented Programming to Callback Functions..

.. or the other way around!

I was reading this nice blog post, and wanted to quote the following part:
From what I know, the original motivation of putting functions inside objects was to support GUI applications. You click on a button and some function (a callback) will be invoked. For the convenience of referring to the button, the callback takes the triggered object as its first argument. Since the callback does nothing more than this, it seems to be convenient to just store it inside the button. And thus we had an “object” which combines the attributes of the button and a method (the callback). Indeed this is a good idea, but this limited usage case can’t really justify a universal notion of "everything is an object".
and then one thing let to another and I found myself wanting to quote this great answer..
I'm stunned to see so many intelligent people failing to stress the reality that the word "callback" has come to be used in two inconsistent ways.
Both ways involve the customization of a function by passing additional functionality (a function definition, anonymous or named) to an existing function. ie.
customizableFucn(customFunctionality) {
    var data = doSomthing();
Though this kind of injected functionality is often called a "callback", there is nothing unforseen about it.
But this is fundamentally distinct from the use of "callback" functions for asynchronous programming, as in AJAX or simply in assigning functionality to user interaction events (like mouse clicks). In this case, the whole idea is to wait for a random / unpredictable event to occur before executing the custom functionality. This is obvious in the case of user interaction, but is also important in i/o (input/output) processes that can take time, like reading files from disk. This is where the term "callback" makes the most obvious sense. Once an i/o process is started (like asking for a file to be read from disk or a server to return data from an http request) an asynchronous program doesn't wait around for it to finish. It can go ahead with whatever tasks are scheduled next, and only respond with the custom functionality after it has been notified that the read file or http request is completed (or that it failed) and that the data is available to the custom functionality.
Asynchronous use inherently involves some means of listening for the desired event (e.g, the completion of the i/o process) so that, when it occurs (and only when it occurs) the custom "callback" functionality is executed. In the obvious AJAX example, when the data actually arrives from the server, the "callback" function is triggered to use that data to modify the DOM and therefore redraw the browser window to that extent.
To recap. Some people use the word "callback" to refer to any kind of custom functionality that can be injected into an existing function as an argument. But, at least to me, the most appropriate use of the word is where the injected "callback" function is used asynchronously -- to be executed only upon the occurrence of an event that it is waiting to be notified of.