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

Here is Why You Need An Adapter

The outlet and plug type used in Saint Barthélemy are C and E and in Samoa is I. This is how they look like.

Samoa

In Samoa, outlets of type I are in use.

Type I

Saint Barthélemy

In Saint Barthélemy, outlets of type C and E are in use.

Type C

Type E