Enterprise software is vital for the survival of the organization. Obviously what qualifies as mission-critical is very specific to each organization. For example, a 3D studio would argue that graphic packages are mission-critical. Still, in most cases, the backoffice is the mission-critical software. The ability to order goods, invoice for products or services, manage stock, etc. is what makes or breaks most businesses.
Departmental software is essentially all the rest.
The distinction is interesting because it helps us think about software in the enterprise. Until recently departmental software is where all the fun has been. It has effectively enabled developers to create better software in less time. And better software in less time is what they have created. They are, by and large, very successful.