Usefulness VS. Usability.

So after giving my brain sometime to digest the reading about clarifying affordances, I am still somewhat confused when it comes to the concept of usefulness vs. usability of design. To me it seemed that usefulness and usability are one in the same, but it is clear in the text that this is not the case, as the author talks about differentiating between these two aspects of design.

After rereading I noticed a sentence in the text that said:
"The designer cares more about what actions the user perceives to be possible than what is true."
This lead me to believe that what the article is trying to say, is that usability is related to what you think the object will do, and usefulness is the actual affordance of the object, or what it actually does. As of now, this is the best conclusion I can come up with, but it still doesn't feel like much more than an educated guess.

Even though I feel like I may have wrapped my mind around the concept of these two different aspects of design, I still don't know if I see the point in differentiating between the two. Is it possible that Gibson and Nelson, and all of the other scholarly people who have tackled the concept of usefulness vs usability have simply over thought the matter? Allow me to explain.

The Merriam-Webster dictionary defines usefulness as "the quality of having utility and especially practical worth or applicability". The same dictionary defines usability as "convenient and practicable for use". Now, maybe I am missing something, but it seems to me as though these two words mean pretty much the same thing! So how is it that you can form to different design concepts out of synonyms?

It is totally possible that I am over thinking things, but I am still interested in discussing this subject with others, and seeing if anyone else agrees, disagrees, or just thinks that I am fixating on a non-issue. I'm not sure if anyone else in the class will read this, but if you do, what is your take?