The Processor clock is also known as the Shader clock and measures the speed of the CUDA cores, hence the processor nomenclature. On the 500 series it is double the core clock, which is also known as the Graphics clock.
On the GTX 560M, apparently the Graphics (core) clock is 775 mhz (half the Processor/shader clock). On the Kepler-based 600 series, the graphics/core and processor/shader clocks are the same. Some lower end 600 series cards are Fermi based and they will have "hot clocks" (shaders clocked at 2x the core).
Processor and Graphics clock are rarely used in favor of core, shader, and memory clock labels.