A Police Complaint is initial reporting of any crime or offence.
It is a narration of facts about the incident in laymans words.
Many a times police complaints will not show against your records.
Whereas in a FIR ( First Information Report) It relates only to cognizable (criminal) offences. Police complaint can be cognizable or non-cognizable offences.
When you file a police complaint in India.. The police will review the complaint and determine whether or not to open an investigation.