Often times, transatlantic states will openly cooperate in military operations, but when such cooperation appears to go against laws, customs, or political and strategic interests, these states either stop cooperating or decide to cooperate covertly via their external intelligence agencies.
Consequently, the determination of whether a specific covert action is related to espionage or warfare has important legal, moral and policy consequences, e.g. concerning assignations and extrajudicial killings.
In the United States, as long as the national intelligence budget was totally classified, the Department of Defense ran many small special operations through the CIA, hiding the costs in the more opaque budget. Now, that both national and defense intelligence budgets are more transparent, there are calls to have small paramilitary operations be fully run by the Dept. of Defense. The problem is that the Dept. of Defense is a larger and thus slower organization.
It seems that the covert operation/overt military operations nexus has not been fully explored by social scientists. The literature seems to have a gap when it comes to explaining transitions from overt to covert military operations, and vice versa. This seems especially true concerning non-anglophone states. If you know studies of this type, please contact me or post them in the comments section.