For what it is worth...

FID refers to the participation by civilian and military agencies of a government in any of the action programs taken by another government or other designated organization to free and protect its society from subversion, lawlessness, insurgency, terrorism, and other threats to their security. The
focus of all US FID efforts is to support the HN’s program of internal defense anddevelopment (IDAD). FID can only occur when there is a HN that has asked for assistance. The US will generally employ a mix of diplomatic, economic, informational, and military instruments of national power in support of these objectives. Military assistance is often necessary in order to provide the secure environment for the above efforts to become effective. For example, a FID program may help a HN to improve the capability or capacity of one of its programs such as counterdrug activities or quell the nascent stages of an insurgency.

FID may or may not include countering an insurgency. When FID includes countering an insurgency, COIN is part of FID. COIN only refers to actions aimed at countering an insurgency whereas FID can aim at dealing with any one or a combination of subversion, lawlessness, and insurgency. In most
cases, the joint force conducts COIN as part of a larger FID program supporting the HN government. COIN that is not part of FID is an uncommon situation, and it should be a transitory situation where the US and any multinational partners should work to establish or reestablish HN sovereignty. The military instrument of FID includes direct, indirect, and combat. This can cause confusion as a lot of folks use U.S. FID and the military instrument of FID interchangeably, which is not correct.