"Application Management is responsible for managing applications throughout their lifecycle. This ITIL process plays an important role in the application-related aspects of designing, testing, operating and improving IT services, as well as in developing the skills required to operate the IT organization's applications. 'Application Management' is an ongoing activity, as opposed to 'Application Development' which is typically a one-time set of activities to construct applications." From here.
"The primary goal of ITIL Configuration Management is to identify, maintain, and verify information on IT assets and configurations in the enterprise. It is one of the areas that comprise ITIL Service Support." From here.
In human words - Application Management are activities how to manage applications lifecycle (requirements, design, implement, test, build, deploy, operate, optimise). Configuration Management is process of identifying and defining logical and physical aspects of an item.
In general I would agree with your company. First you identify and define the item and then you can manage it.