From my understanding they are different. Linux framebuffer is a software object and GPU's memory is a physical memory mapped to GPU device.
My questions are the following:
1) Is my understanding correct?
2) If so, somehow merging two things into one looks like possible to improve the performance (I guess there are much more technical details why this is not possible and so on...)
3) If not, could you explain how Linux framebuffer and GPU work together?