Speculatores and Exploratores were the scouts and reconnaissance element of the Roman army. In both the legions and in the praetorian camp, speculatores were initially scouts but became bodyguards, couriers, law-enforcers, and sometimes executioners. Exploratores were tasked to keep watch on enemy movements in the field. Both occupations could require the wearing of 'plain clothes' and may therefore be deemed spies (Occulta speculator/speculatrix). The Roman Empire lasted a very long time and various espionage units, including the infamous frumentarii created by Hadrian to suppress internal dissent, and later the agentes in rebus, came and went throughout its history.
The first permanent imperial bodyguards were the Corporis Custodes (also called Germanic or Batavian bodyguards). They were probably involved in the death of Emperor Nero, and therefore from that moment on amortized as bodyguards.
His successor, Galba, promoted his own bodyguards, the Speculatores, to imperial bodyguards. This situation continued until emperor Trajan promoted his own bodyguard, the Equites Singulares, to imperial bodyguards.
The Speculatores were recruited from the best riders of the Praetorian cavalry; they became the unit that was entrusted with the protection of the emperor in Rome. Despite being a private, standalone unit with its own barracks, the unit frequently counted to the Praetorian Guard.
The tasks of the imperial bodyguard consisted of (among others): guarding and protecting the emperor, the delivery of imperial mail and training with the emperor during public shows, in which the emperor could show his riding and combat skills to the population.