A video card with 1GB of RAM usually has slower RAM than a video card with 512MB of RAM.
That is changing in the mid-high grade video cards. I've noticed some manufacturers trying to compensate for a lower core clock speed with slightly higher speed memory.
Mine does have several gigabytes built into it two as displayed in game
This is where you are quite wrong. From your dxdiag report you can see what memory there is
available to your graphics card to use. As previously stated, DirectX 10 and 11 don't report just the actual physical memory onboard your video card, system memory is now also included, just like DirectX 9 did with onboard video chips that used system memory.
Display Memory: 4071 MB <--- that is the total amount of memory (graphics card and system) that is allocated by DirectX for use in graphics processing on your system if it needs it.
Dedicated Memory: 1012 MB <--- that is how much actual physical memory is on your video card.
Shared Memory: 3059 MB <--- that is how much of the 8 gigabytes of your system memory DirectX will use if needed.
Now apply what Skuzzy said about the textures being moved from video to system memory.
