The Processor is the CPU. This is the component that you can change on a motherboard and does all the number crunching with the help of the chipset.
The chipset is the Northbridge & Southbridge chips and these are high speed connections to the RAM, GPU, I/O, etc.
Consider this motherboard
The chipset on this motherboard is the AMD 790GX + SB750.
becomes part of the chipset on the motherboard when added to the motherboard.