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

Here is Why You Need An Adapter

The outlet and plug type used in Anguilla are A and B and in South Korea is F. This is how they look like.

South Korea

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

Type F

Anguilla

In Anguilla, outlets of type A and B are in use.

Type A

Type B