Answer:

The difference between a linear and a nonlinear cost function is

A linear cost function is a cost function where, within the relevant range, the graph of total cost versus the level of a single activity related to that cost is a straight line.
An example of a liner cost function is a cost function for use of a telephone line where the terms are a fixed charge of $10,000 per year plus a $2 per minute charge for phone use.

A nonlinear cost function is a cost function where, within the relevant range, the graph of total cost versus the level of a single activity related to that cost is not a straight line.
Example include economies of scale in advertising where an agency can double the number of advertisements for less than twice the costs, step-cost functions, and learning-curve based costs.