Short answers, pulled from the story.
The Police of Russia, known as the politsiya, is the primary law enforcement agency. It is subordinate to the Ministry of Internal Affairs and provides public security functions. It was formerly called the militsiya before being renamed.
The FSB is Russia's main domestic security agency, responsible for anti-terrorism operations and internal security. It is the main successor to the Soviet-era Cheka, NKVD, and KGB. The Federal Border Guard Service is also subordinate to the FSB.
The Investigative Committee of Russia is the main investigative body and is sometimes described as the "Russian FBI." It operates as a separate agency from the Police of Russia.
Prisons in Russia are administered by the Federal Penitentiary Service (FSIN) under the Ministry of Justice. Facilities are divided into four types: pre-trial institutions, juvenile labor colonies, corrective labor colonies, and prisons. In 2004 there were 760 corrective labor colonies, eight prisons, 62 juvenile facilities, and 192 pre-trial institutions.
Russia's National Guard was formed by consolidating the former Internal Troops, OMON, and SOBR units. It performs a gendarmerie function, handling large-scale riots and internal armed conflicts, and provides security for high-priority facilities such as nuclear power plants.
The Presidential Security Service handles tasks specifically related to protecting the President of Russia. It operates alongside the Federal Protective Service of Russia, which has a broader mandate covering state property and all high-ranking government personnel.