Final answer:
The agreement between the Air Force and a Navy detachment for support is an Inter-Service Support Agreement (ISSA), outlining logistical support and resource sharing for effective operation.
Step-by-step explanation:
The type of support agreement commonly made between different branches of the U.S. military, such as the Air Force and a Navy detachment, is known as an Inter-Service Support Agreement (ISSA). These agreements are essential for outlining how different branches will support one another, especially in joint operations or in circumstances where one service may have resources that another needs. These agreements include details on the provision of logistical support, resources like equipment and technology, training, intelligence sharing, and more. It is a practical approach to ensure that both services can operate effectively while sharing capabilities and enhancing overall mission success.