What is the difference between many core and multi core?
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.