You Do Need power plug adapter while traveling from Vatican City to South Korea.

Here is Why You Need An Adapter

The outlet and plug type used in South Korea is F and in Vatican City are C, F and L. This is how they look like.

Vatican City

In Vatican City, outlets of type C, F and L are in use.

Type C

Type F

Type L

South Korea

In South Korea, outlets of type F are in use.

Type F