I'm not so sure that it strictly does. There is a long relationship between the "civilian" western intelligence services and the military even if they are not technically branches of the armed services. Every director of the NSA has been a serving military officer. The first four directors at CIA were. The Defense Intelligence Agency is under the auspices of the Pentagon. Both British domestic and foreign security/intelligence services emerged from the military and remain best known as MI5 and MI6, the MI standing for military intelligence.

Others can probably answer as to the evolution of the Soviet side but I would question the premise.

Edit: typo