Short Answer
Multicore - multiple cores in just one die.
Multiprocessors - More then one processor and each one in separate die.
Detail Description
A multiprocessor system contains more than one such CPU, allowing them to work in parallel i.e Simultaneous Multiprocessing.
A multicore CPU has multiple execution cores one one CPU which means that a certain subset of the CPU's components is duplicated, so that multiple "cores" can work in parallel on separate operations. This is called CMP, Chip-level Multiprocessing.