dear student

Production engineering basically deals with the manufacturing process based engineering such as fabrication, machining, casting , forging etc. 

Industrial engineering has only one motive, I.e. to increase productivity( output to input) of an industry by designing techniques developed from scientific methods of engineering. It includes Time and motion study where a qualitative and quantitative evaluation of a work is carried out.

basically its a technical & management approach.

hope it helps

All the best!!!