Written statements like the ones you referenced can do a lot of work in building and reinforcing how the identity of a group of people is understood by individuals outside of the group. These statements intend to show people outside of the Caribbean what Caribbean culture is like. However, they aren't really trying to show the complete Caribbean identity. Rather, they're showing us specific aspects of the identity. They seem like they came from an advertisement that's trying to get tourists excited about Caribbean culture so that they'll come to visit.
The first line is "The Caribbean, wish you were here!" The "wish you were here" with an exclamation point conveys a sense of openness and optimism that they want to share with others. It makes it sound like the Caribbean is an exciting place where lots of fun things are happening.
The next line is "We're more than a beach, we're a country!" With this line, the writer wants to convey that there's more to the Caribbean than beaches. Again, this seems targeted to tourists who might be looking for more than just another beach vacation.
Next, "We are as different as we are alike" and "This is what makes us Caribbean!" These lines convey that the Caribbean identity is a diverse one, as well as one that's built on shared similarities. They want to share that they're a diverse group of peoples who are united in their diversity.
As stated above, these lines read like an advertisement to tourists. That tells us something about Caribbeans too. They're a group of people who welcome tourists, who probably rely on tourism to sustain their economy, and who have a sense of marketing and business acumen. Overall, the lines express a Caribbean identity that is warm, friendly, and diverse.