Innovation is developing a new method, product or Idea.
Example: New innovation has developed an artificial heart device to extend a person's life.
Productivity is not developing (innovating) something new. It is the amount of products made, usually in a set amount of time.
Example: A company builds 25 computers a day. (Low Productivity)
A company builds 25,000 computers a day. (High Productivity)
Note: If the company only has one employee, maybe 25 computers is high productivity.
Productivity is based on the situation.