A Quad-core processor is a chip with four independent units called cores that read and execute Central Processing Unit instructions.
The instructions may be addition, movement of data, and branching.
Within the chip, each core operates in conjunction with other circuits such as cache, memory management, and input/output ports.
A multi-core processor is a computer processor integrated circuit, with two or more separate processing units, called cores, each of which reads and executes program instructions as if the computer had several processors.
The individual cores can execute multiple instructions in parallel, increasing the performance of software which is written to take advantage of the unique architecture.