You Do Need power plug adapter while traveling from South Africa to Western Sahara.

Here is Why You Need An Adapter

The outlet and plug type used in Western Sahara are C and E and in South Africa are C, M and N. This is how they look like.

South Africa

In South Africa, outlets of type C, M and N are in use.

Type C

Type M

Type N

Western Sahara

In Western Sahara, outlets of type C and E are in use.

Type C

Type E