From the sound of it, it sounds like you're trying to say, there's no difference. I think it's clear that there's a huge difference between being able to recite an answer from a book, and being able to understand it well enough to interpret it in new situations, because life doesn't offer problems that are set up neatly for you. A really simple example I can think of is the number of persons I knew in the 90's who could not grasp something as simple as a computer file - so a feature like a file directory structure made no sense to them at all. They thought the only way to see a file was to open the application they created it in.
My mom could only solve math problems if the problem was asked in a way where she was given a formula and the variables were NAMED in the problem. She really had no idea what it meant. I have the same challenge teaching math to my youngest, who still doesn't grasp simple arithmetic - she guesses, because it might as well be spells and witchcraft.
One of my very favorite books is an autobiography of sorts by the physicist Richard Feynmann - I say, of sorts, because it's clear that it's more of a collection of parts of his life arranged in chronological order, such as lectures or stories he told others, but doesn't really appear to be intended to tell his life. And in one of the chapters, he tells of his time teaching in Brazil.
Here, I found a link to that section --
Go ahead, he's amazingly readable, but it perfectly encapsulates my concept - knowing the material, but not at all understanding it in any way.