The simplest difference is that design is theory and manufacturing is practice.
Chip design and chip manufacturing are very different, chip design is in a chip on which position should be placed what things, reasonable arrangement of chip position. And chip manufacturing is the design of this chip pattern, through technology to manufacture. Design is just a pattern drawn by the brain, and manufacturing is to make a complete chip through this pattern with the help of technology and a machine.
Designing a chip is like writing on paper, very. Easy, but making chips is very difficult.