For most purposes there is no difference. The NKVD was effectively the successor to the OGPU, following a reorganisation in 1934. 'NKVD' without a qualifier almost invariably refers to this later body. My advice to most people is to leave it at that and treat the series of four-letter acronyms as, more or less, synonymous and in sequence.

However, if you really want to dive into the alphabet soup that is Soviet security agencies then there are actually a few differences to be aware of, particularly for the 1920s. Let's start with the definitions, below.

You may want to keep in mind the distinction between all-union level (ie across the entire USSR) and republic level (ie one of its constituent republics, including Russia). Also, the 'militia' are the regular uniformed policemen who deal with mundane (ie non-political) crimes.

• NKVD RSFSR - People's Commissariat of Internal Affairs of the Russian Soviet Federated Socialist Republic (1917-1930): Established post-October, this ministry was responsible for 'regular' policing (the militia) in the Russian republic only. It did not include political policing or counter-revolutionary activities. This was the responsibility of...

• Cheka - All-Russian Emergency Commission for Combating Counter-Revolution and Sabotage (1917-1922): The body responsible for political policing and key instrument of internal repression during the Civil War.

• GPU - State Political Administration (1922-23): A rebranding of the Cheka, in which it was placed under the NKVD RSFSR. So, again, responsible for political policing. This was short-lived for Russia but local GPUs continued to function at republic level, as regional branches of the OGPU.

• OGPU - Unified State Political Administration (1923-34): With the creation of the Soviet Union, the Cheka/GPU was detached from the NKVD RSFSR and made an all-union body. Until 1930 it was only concerned with political policing, with regular policing remaining at republic level. In 1930 republican NKVDs were abolished and responsibility for the militias transferred to the OGPU as a central inspectorate.

• NKVD USSR - People's Commissariat of Internal Affairs of the Soviet Union (1934-1946): This was the product of the OGPU's victory in the bureaucratic battles of the 1920s: the annexation of all security functions into one body. The new NKVD had control of regular policing, political policing, the penal system, fire departments, border troops, security economic concerns, etc. Political policing was reconstituted within the NKVD as GUGB (Central Administration of State Security).

That brings us up to the war and leaves out large chunks of the internal administrative reorganisations that these bodies went through. After the war there was another major round of splitting, with political policing being split off again into an iteration of the infamous KGB.

So, to actually return to your question on the GPU, it depends on the time period. For most of the 1920s the split you're likely referring to is between regular policing (NKVD RSFSR) and political policing (GPU/OGPU); it wasn't until the 1930s that these functions were formally unified.

Clear as mud?