I actually went back and read that Wiki article, and as usual, it is awful.
Physical chemistry isn't too bad if you've had the prerequisite linear algebra. Many people haven't and that is where the trouble comes from. It can be a bear if you have to pick that up on the fly.
Organic chemistry, on the undergraduate level, is memorization of reaction mechanisms with a few basic applications of math. On the graduate level, it is a different animal. Combine undergraduate organic chemistry and physical chemistry to get a better idea.
Biochemistry can be looked at as an easier version of organic chemistry. At least that was true when I took it. Memorize proposed reaction mechanisms, but these mechanisms aren't advanced far enough along so that you'd have to deal with much math. This is changing, probably. It certainly has changed a lot in the upper levels in the past 5 years with the shift in focus to what they call the genetic environment.
To answer your question, PeteCO, physical chemistry is sometimes called chemical physics. It deals with a lot of quantum theory and that sort of thing. Organic chemistry deals with carbon-based molecules. Most of these are man-made in the sense that organic chemistry deals with them, but many occur in nature also. The organic connection comes in because of the carbon. Biochemistry is biological chemistry. Basically the chemistry that occurs inside living things. Those are the short and practical definitions, at least.
Carbon nanotubes did originally fall under organic chemistry but have largely moved into their own. Nanomaterials is a big deal because much of the basic theory has been worked out and the properties of some basic nanostructures have already been extensively studied. It is primarily an engineering problem at this point to get these things into economical production. Of course, there are plenty of theoretical advancements to be made. Don't get me wrong. These things are just getting really close to practical. A lot of chemistry and chemical engineering programs are running into this at full speed because they've caught the scent of money...that is the academic world for you. I've been poking around the edges of this for a couple of years but haven't really had the ability to get deeply involved until now.
Contrast this to fuel cells, which are a long way from any common application since a lot of theory still has to be worked out to make them better than many of the alternatives. A lot of the problems facing fuel cells are more than just engineering problems.