I think most people confuse between the two. This is true especially for laymen who do not go through the rigorous study in physics.
Learning physics is defined as what we normally have in a university setting. There's a series of information, understanding, discourse, skills, and even interaction that are all involved in learning physics. Physics, as is true for a number of other subject areas, isn't a passive subject that you can just and think you have understood what you've read. I can tell you that F=ma, and even define what those symbols mean, but I can guarantee you that if this is your first time seeing it, you'd never be able to use that equation to solve the problem of how much load is being supported by a structure. just simply reading a physics text give you only a superficial knowledge of the material. Until you can use it to solve actual problems and see how it is applied or how it work, then you can say that you've understood it. Physics involves knowledge AND skills, and in this case, it is the skill to think about something and to know how to solve it. These are the steps involved in learning physics.
Learning ABOUT physics is different. You can pick up one of the popular pop-science books and learn about physics. Since these books almost have no mathematics, physics principles are often illustrated either via analogies, or via specific examples. While this technique is perfectly fine, what is missing here out of necessity is that the reader does not see the most general form of the principle, which in all cases can only be described in the clearest way in mathematical forms. For example, try to explain what Gauss's law is. You can attempt to say:
The sum of all the electric field crossing a closed surface and perpendicular to that surface area is proportional to the amount of enclosed charge within that surface.
You'd get blank stares looking back at you. So instead, you either use an example (point charge is popular), or you use analogies (water flowing out of some opening or source).
Now this is perfectly fine. Unfortunately, in many cases, the person reading or hearing such a thing often either forget, or overlook the fact that these are analogies or special cases. If he/she sees another example, he/she might not know that this really did come from the same principle. Or worse still, he/she thinks that that example is IT, and that the principle is only represented by that example. They start thinking that the example IS the principle. Just look around the 'net and see how many people think quantum mechanics is nothing more than the uncertainty principle, or wave-particle "duality". They seem to have missed that all of these came out of a set of starting points, including the QM postulates and how QM treats observable operators. The uncertainty principle and others are simply consequences of these starting points. So in other words, they only saw the shadow of the animal and think that this IS the animal!
The reason why I'm writing this is that I've encountered another case where someone with only a superficial knowledge of physics and who got it by reading pop-science books (in this case, Hawking's "A Brief History of Time") seems to think that he knows as much physics as I do. One can already imagine how frustrating it can be when dealing with such a person. When you try to show where he made a mistake, he often "quote" passages from the book and then tries to extol the prestige of Hawking ("He's a world famous physicist. He can't be wrong here!").
There's nothing wrong in wanting to know a bit more about physics via reading such pop-science books. Heck, I've even recommended many of my friends to a few of them. The error here is in deluding oneself into thinking that, even if one understood everything that's written in these books, that one has learned physics. This is wrong. What one has learned is something ABOUT physics, rather than physics itself. Try to solve a typical physics problem using what one learned out of these books. This would be a very clear test of one's knowledge. Learning about physics gives one a brief glimpse of physics. It should never be confused with an actual learning of physics.