#1. Constitutional Bodies are formed by the Constitution which helps the Government to run properly.
Some Important constitutional Bodies:
1. Union Public Service Commission (UPSC)
2. Staff Selection Commission (SSC)
3.National Human Rights (NHR)
#2. An extra constitutional body is an institution of government which is not defined in Constitution of India but are established by a resolution(decision) of union cabinet. For Example Planning Commission, National Development Council etc. They are created by various methods which further explain their nomenclature.
#2A. Statutory Body: They are those bodies which are created by a law passed by the parliament which explicitly mentions the objectives for creation, their composition, Powers. Such bodies are subject to change by a respective change in the law governing them.
Example: National Human Rights Commission(formed to conform to United nations charter on Human rights), Central Vigilance Commission, National Biodiversity Authority etc. (formed out of the Biodiversity Act, 2002)
#2B. Executive bodies: they are those bodies which are created by an executive order – i.e. order of a ministry of union or state. Such bodies have no constitutional or law backing them. One very infamous body was Planning commission (now replaced by NITI aayog).
Other such bodies are UIDAI (Aadhar card), which when faced controversy is undergoing shift to statutory body.