The official management decision given by a senior organizational official to authorize operation of an information system and to explicitly accept the risk to organizational operations (including…

Authorization (to operate), often referred to as ATO, is the formal decision by an authorizing official to accept the residual risk of operating an information system. This process confirms that the system's security controls are deemed sufficient and that the organization is willing to bear any remaining risks.

Systems operated is a generic term that does not represent a specific formal decision or process in risk management.

Security Authorization is a broader term that encompasses the entire process leading to an authorization decision, but Authorization (to operate) is the specific decision itself.

Senior Organizational describes a position or a type of official, not the decision being made.