adjectives - Use of [any other] in a sentence

The Nile is longer than any river in India.
The Nile is longer than any other river in the world.

In both of these above sentences, we are comparing one river with the rest. But still we have used any other in second and any in first sentence. Any rules regarding this usage please.

Answer

'Any' is applicable when we compare anything that is not a member of the group compared.

Said that,

The Nile is longer than any river in India. (The Nile is not an Indian river.)

If you use the Ganges instead of the Nile, you need to write the above sentence as:

The Ganges is longer than any other river in India. (The Ganges is an Indian river.)

So, 'any other' is used when we compare anything that is a member of the group compared.

In your example, as The Nile is a member of the group of rivers in the world, the second sentence requires 'any other' instead of 'any':

The Nile is longer than any other river in the world.