You Do Need power plug adapter while traveling from Botswana to Nauru.

Here is Why You Need An Adapter

The outlet and plug type used in Nauru is I and in Botswana are D and G. This is how they look like.

Botswana

In Botswana, outlets of type D and G are in use.

Type D

Type G

Nauru

In Nauru, outlets of type I are in use.

Type I