word choice - What is the difference between 'east Indian' and 'eastern Indian'?

I read the following line in NYT:

A surging crowd near a Hindu temple killed at least ten people and injured 25 others in the eastern Indian state of Jharkhand on Monday, police said.

Now, my questions regarding this line are:

1. Can we write 'the east Indian state' instead of 'the eastern Indian state'? What is the difference between them?


2. Which one is more preferable? In India, I have come across many sentences with 'east Indian state' clause.