Production is defined as a process or procedure to transform a set of input to output having the desired utility and quality.
To the production people, Production is the quantity produced by the batch or a line irrespective of input. Like a line supervisor reports as daily production to management (e.g. Yesterday’s production of line-x is 500 pieces).
On the other side, Productivity is the ratio of output and Input.
Some of usage of Production term is: Production of cutting department, or production of the sewing line-X. etc.
Example: Suppose sewing line y has produced 400 pieces by 35 workers in a day.
Production of the line is 400 units. (This is just the quantity. Input has not been considered here. You don't know how many machines or labors is utilized to make this much quantity.)
On the other hand, productivity (labor productivity) = 400/35 = 11.42 pieces per labor per shift.
(To find labor productivity labor input is considered. You measure the performance per labor. With the productivity figure you have clear idea about the performance of the line.)
This is a tiny part of the book Industrial Engineering Guide to Job Interview Preparation. Read the book.
Also see: How to measure labor productivity?