CID is a standard acronym for Criminal Investigation Division in just about any English speaking military. It's the investigative branch of the military police. It's the most used definition for the acronym CID in the world.

Likewise is CBI, but on a civilian level as opposed to the military. Criminal Bureau of Investigation or Central Bureau of Investigation. Like the FBI - Federal Bureau of Investigation.

There are quite a few of semi-related organizations that use the acronyms CID & CBI. The Criminal Invertigations is just the most common.
Central Bureaus of INvestigation,
Crime investigation department,
CBI is a vast organisation compared to CID, they are different organisations but they are complemetary toooooo