People confuse the terms and often don't make the proper distinctions:
MULTI-PROCESSOR: More than one physical CPU (meaning the mother board has more than one socket)
MULTI-CORE: Means that a single CPU has more than one processor core inside of it. But it is still a single physical 'chip'.
DUAL-CORE: Is a Multi Core CPU that has two processing cores in it
QUAD-CORE: Is a multi core CPU that has four processing cores in it.