These terms seem to be same but in a guest lecture i found that they are not but i have not been able to find the difference even after googling around for a while .
Multicore typically refers to devices with 2-8 or so cores in them.
Manycore typically refers to devices with dozens or hundreds of cores.
As far as I know, there's no hard definition of when you go from a multicore to manycore device. My guess would be that the words were defined by someone's marketing department...
One difference between them is that manycore systems will only run efficiently with software that is designed with multiple cores in mind - single threaded software will be extra slow on such equipment.
Multi-core: A system with 2-8 cores and particularly does not implement parallel architecture (either at HW or SW)
Many-core: A system with hundreds or thousands of cores and implements parallel architecture (HW and SW).
A cluster may be made of Multi-core and Many-core systems.
Multicore: Main the execution speed of a sequential program.
Many-core: Maintain Execution throughput of a parallel application