Dignitary Protection
Dignitary Protection services are most often provided by either the United States Secret Service or the US Department of State’s Diplomatic Security Service.
Secret Service
In addition to US government protectees (the president and other members of the Cabinet), the Secret Service protects visiting heads of state.
Diplomatic Security Service
In addition to US government protectees (the Secretary of State, the ambassador to the United Nations), the Diplomatic Security Service protects foreign dignitaries who are not heads of state, essentially everyone else.
In recent years DSS agents have also protected foreign leaders in their own country. This includes the president of Liberia, and the president of Afghanistan.
Other agencies
In the United Kingdom this type of protection is commonly referred to as close protection.