You Do Need power plug adapter while traveling from Belize to Samoa.

Here is Why You Need An Adapter

The outlet and plug type used in Samoa is I and in Belize are A, B and G. This is how they look like.

Belize

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

Type A

Type B

Type G

Samoa

In Samoa, outlets of type I are in use.

Type I