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.

>>20
Yes and no.

Yes, it has a pile of fancy tech, and long-timers in that industry really know their stuff. AI, graphics, UI, physics, audio, networking, and all performance too! Oh my...

But no, some parts (emphasis on some) of the business domain take the Right Stuff (TM). Unlike in gaming, if something goes wrong, you might be losing millions per minute. There's also that niggling problem of scalability.