What is the difference between directors and officers liability insurance and public and product liability insurance?

The operational field of the two categories differs.  The liability insurance for the guy on the ground would thus more than for directors but the guy on the ground does not accept liability the directors do

D&O liability is concerned with a liability coming from D&O actions that lead to a monetary loss affecting the stockholders, or not working in their favor.

Public&Product is concerned with the core business of a firm and the possibility of that product to cause a loss.