What is the difference between a multiprocessor and a multicore system?

What is the difference between a multiprocessor and a multicore system?

Each core in a multicore system shares components such as processors, registers, and the ALU.

Each core in a multicore system acts as an independent processor

Each processor in a multiprocessor system has independent access to main memory and I$/$O facilities

Each processor in a multiprocessor system is interconnected by a bus $($or other internal connection scheme$)$ that allows different memory access time between processors.