The proper noun Caribbean refers to the region of the Caribbean Sea. The word is widely used as an adjective to refer to people of things in or from the region. The noun Caribbean can also refer to a native Carib islander.
When a proper noun is used as and adjective, it is a proper adjective; for example:Ancient Mexican structures have similarities to ancient Egyptian structures.
They are all nouns, Caribbean being a form of "Caribbean Sea" or "Caribbean region." But Caribbean can also function as a proper adjective (Caribbean tribes, Caribbean music).*The word island is usually considered a noun adjunct (attributive noun) when used with another noun, e.g. island paradise, island map. This also applies to location in location scouting and reunion in reunion committee.
The proper adjective for Portuguese is "Portuguese."
The proper adjective for Haiti is Haitian.
The proper adjective for southwest is "southwestern."
Vietnamese is the proper adjective for Vietnam.
The proper adjective for George is Georgian.
The proper adjective for Siam is Siamese.
Freudian is the proper adjective for Freud.
The proper adjective for Georgia is Georgian.
The proper adjective for Mayan is "Mayan."