They are different. A processor is the central processing unit (CPU), while a CPU or ‘Chip set’ is an integrated circuit that contains this, as well as other units like the memory controller and bus interface.
The term “CPU” has replaced many of the industrial-era terms like “mainframe”. For example, it was common in the industrial age to talk about CPUs belonging to manufacturers like IBM or Burroughs; today these would be called simply MacPros (corporation) processors because there’s only one such company left.