Graphics card memory is independent of system memory. The "on-board" graphics card memory is used for higher level graphic processing and resolution rendering.
System memory is what your computer programs and processes are loaded on to. The hard drive transfers the functions to this RAM.
Checkout this article on the difference in RAM usage between 32-bit Windows and 64-bit Windows:
The most significant advantage of a 64-bit system is that it can use more than 4GB of RAM. One thing that has changed since I last concerned myself with this topic is that most new desktops and laptops now come with at least 4GB of RAM. The problem is that like Vista, Windows 7 x86 is capable of only using about 3 GB of RAM. By contrast, Windows 7 x64 cannot only make use of up to 16TB 192GB RAM, but is capable of using the memory remapping feature of modern BIOSes, which allows the operating system to really use the complete 4GB. Thus, if you install Windows 7 64-bit on a 4 GB machine you won’t waste 1 GB of RAM like you would with Windows 7 32-bit.