Difference between a CPU and control unit?

There is a big difference between these components. Both of them are part of central processor unit but control unit is responsible for generating control signals to all parts of cpu, to handle interrupts, to deal with registers etc. Arithmetic logic unit is part which does arithmetic and logic operations (for example, arithmetic operations are add,subtract,add with carry,subtract with carry,divide... and logic operations are AND,OR,XOR,NOT,NAND,NOR...).