"Graphics driver" can mean any number of things.
The way X (the graphical windowing system) works is that there is a central X server, which can load modules ("X drivers") for different hardware. Like
Some of these drivers can work on their own (
vesa). Some need linux kernel drivers. Many of these kernel drivers following the "direct rendering manager API", and therefore they are called "DRM drivers". Others, like the proprietary
nvidia driver (which needs both an X driver and a kernel driver), don't.
It gets more complicated: The hardware consists of parts that read out the framebuffer and display it at different resolutions etc. This is called "modesetting". Modern graphics card also have a GPU, which is used to accelerate 3D drawing (OpenGL). "DRM kernel drivers" provide an interface for both.
"Mesa" is a software library that understands OpenGL, but does the rendering either on the CPU, or on some (but not all) GPUs (see here for a list). So the Mesa library can offer this functionality for graphics card that do not or do not sufficiently have hardware for this, or can serve as the OpenGL library for a few GPUs.
You could probably make a case to call anything in this complex picture a "graphics driver".