Definition of Differential Cost and Incremental Cost
I use the terms differential cost and incremental cost to mean the same thing: the difference in cost between two alternatives.
(I use the term marginal cost when referring to the cost of producing the very next unit or operating for just one more hour, etc.)
Example of Differential Cost and Incremental Cost
Assume a company determined that the annual cost of operating its equipment at 80,000 machine hours was $4,000,000 while the annual cost of operating its equipment at 70,000 machine hours was $3,800,000.
The differential cost and/or the incremental cost of operating its equipment for the additional 10,000 machine hours was $200,000.