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level of force
for national security reasons (movement of troops during a time of war)
their own restraint
There is no difference. In some instances security companies themselves use a distinction of Armed to Unarmed personnel. Guard or security officer refers to Unarmed and Security Enforcement Officer refers to Armed. Each state has different licensing and laws about security personnel.
Usually security enforcement officers for banks and other high risk areas are previous law enforcement officials, but there are training and certification classes available for that job.
The FBI is a Federal law enforcement agency responsible for security and law enforcement in the United States.
security police
Challenging is a physical security measure that is appropriate in certain situations. Places challenging people for security measures is appropriate are prisons and military sites.
The government can exercise prior restraint on the press only in cases of national security or to prevent direct harm, such as risking lives or inciting violence. Prior restraint is generally frowned upon due to First Amendment protections of free speech and press freedom.
The generallized term, "Law Enforcement," does not apply to any single entity of government. Many agencies of government have law enforcement missions and authority, the Dept of Homeland Security is just one member of the entire panoply of agencies that has such a mission.
That is a question for the individual security officer and his employer. However, most law enforcement officers will appreciate the show of observance and respect from the security community for wearing a black mourning band.
The Diplomatic Security Service is the law enforcement arm of the United States Department of State.