C vs. C++

So, I've decided to go ahead and teach myself Game Programming. I picked up a book that seems pretty good for the task (Thompson's "Beginning Game Programming") that deals with the creation of 2D and 3D games using C and DirectX. Now, that's all well and good, but I've never specifically dealt with C before: only C++.

C++ I've learned in several college courses (I'm a Computer Science major), and have completed all the classes offered. These covered the range from Hello World to manually creating Binary Search trees (not using any built-in libraries to do the job for me). I'm fairly comfortable with the language, though nothing I've yet created in C++ used a GUI.

I'm aware that C is sort of a precursor to C++, with more limited capabilities, and much of the syntax is the same. My question for you all is how hard would it be to pick up C having only dealt with its more advanced relative? Is there anything I should know? Any good online resources I should check? (preferrably free)

Thanks for any help you can provide.

If you want to do games then C++ is pretty much the only option because it's fast and is OO. Take a hint from the gaming industry. They all use C++.