Did you actually read the two chapters in the same book to figure out the difference? I'm guessing it's an old book which may be using outdated terminology.
What I can remember from my studies and based on the terminology CPU organisation could mean the different components within a CPU such as ALU (arithmetic logic unit), instruction decoder, cache, clock, registers etc. As for computer organisation, probably the components of the rest of a computer? Such as BIOS, CPU, Volatile storage (Memory/RAM), Persistent storage (Tape/Disk/Optical), interconnection between these components (bus, aka ISA/PCI/northbridge/southbridge etc).
Why don't you read the two chapters and post here the salient points of what each of them contain?
Computer organization was one among d toughest subjects i had gone through in my B.E. Simply said,had to write it thrice to get it cleared or maybe our ma'am avenged the whole class for misbehaving.
Or maybe it was a tough one for everyone in my class with only 12 passing in a strength of 70.
As vishal explained it properly,CO also contains the elementary calculations done within the cpu and many algorithms used in doing it faster.
If u want a better explanation on computer organization the attached syllabus snap might help you.