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

Here is Why You Need An Adapter

The outlet and plug type used in Cayman Islands are A and B and in Saint Barthélemy are C and E. This is how they look like.

Saint Barthélemy

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

Type C

Type E

Cayman Islands

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

Type A

Type B