The term "East Indian" is outdated and potentially offensive. Historically, it was used by Europeans to distinguish people of the Indian subcontinent from the "Indians" of the Americas (after Columbus's error).
The Indian subcontinent comprises:
All are located in South Asia, which is part of the continent of Asia. The preferred, accurate terms are South Asian, Indian (citizens of India), or specific national/ethnic identities (e.g., Punjabi, Tamil, Gujarati, Nepali).