Cajun food is also an attempt to recreate foods from their places of origin.

Acadians were forcibly removed from the Maritime Provinces of Canada by the British. Some were conscripted into the British Navy, others moved to another French settlement in the Americas. The French aristocracy, who lived in New Orleans at the time, wanted nothing to do with the people who were forced out of Canada. They had to leave everything they owned behind and thus were poor because it. This influenced Cajun (Acadian) Cuisine. They made the best they could with what they had and there are Spanish and Native American influences in their original French recipes.

Creole food is started as food made only for the wealthy. Because the French aristocracy of New Orleans owned slaves, that influence in their food is easily distinguishable.

Either way, I think the difference in American Japanese or Chinese food is that it was specifically created according to the expectations and palate of American settlers. Where as Cajun and Creole were attempts to make food they were already accustomed to with ingredients they had on hand while being influenced by other cultures.