The big difference between the FBI and the Gestapo is that Hitler had some control over the Gestapo and they never attempted a coup d’etat.
Putin doesn’t trust the FSB to prevent a color revolution so he set up the Federal National Guard Service to act as an additional check on the FSB and the army.
The FSB doesn’t conceal its origins in the Soviet Cheka.
That, and the FBI originally was a force of good before getting turned for evil purposes since Clinton at the very least, while the Gestapo was pretty much evil from the start.