Section 2 of the Foreign Exchange Management Act, 1999 (FEMA) deals with various definitions. It defines a person resident in India and a person resident outside India. However, it does not define the term non-resident nor it does define the term Non Resident Indian (NRI).
However, Notification No. 5/2000-RB (dealing with various kinds of Bank Accounts) defines the term Non Resident Indian (NRI) to mean a person resident outside India who is either a citizen of India or is a person of Indian origin. In short, the definition of the term NRI is contextual and can have slightly different connotations for FEMA/Income Tax/Acquisition of Immovable Property etc.