"Cajun" and "Creole" are terms you'll see everywhere in New Orleans and South Louisiana. On menus, in particular, but also in discussions of architecture, history, music, and more. But what do they mean?
What is "Cajun?"
The Cajun people are descendants of French-Canadian settlers who first began settling in Nova Scotia -- an area they called l'Acadie -- in 1605. After 150 years of relatively peaceful farming and fishing on the edge of the Bay of Fundy, these people were expelled when Canada fell to British rule.
These people -- Acadians -- scattered. Some hid nearby, often among the Micmac Tribe, with whom they were friendly. Others got on boats: some voluntarily, some not, and sailed away. After a few years of diaspora, they regrouped when they were invited in 1764 to settle in the then-Spanish colony of Louisiana.
These folks, who learned to farm and fish in cold Canadian climes, settled in the swampy, bayou-laced areas to the South and West of the small colony of New Orleans. They regrouped and formed communities, and over the years incorporated cultural influences from their new Native American neighbors, and fellow settlers of German, Irish, Spanish, and English descent, as well as African-descended people, both enslaved and free, and French-from-France folks.
The developing culture was deeply rural, subsisting on fishing and farming in the swampy coastal regions, and beef cattle raising in the inland prairie areas of their settlement area, which covered what is now most of South Louisiana, save the settlements of New Orleans and later Baton Rouge.
The term "Acadian" morphed in English into "Cajun," and was used largely as a derogatory term until it was reclaimed during Cajun pride movements in the mid-20th century.
Cajun people are historically francophone (and many still speak French today, a dialect which is unique but fully mutually intelligible with standard French and Canadian French) and Catholic.
Cajun cuisine is rustic, relying heavily on smoked and stewed meats and seafood dishes and richly spiced but not overly spicy, by the standards of other Caribbean and subtropical cuisines. Rice is the typical starch, but sweet potatoes are also grown in Cajun regions and used in traditional dishes. Cajun music has similarly evolved from traditional Acadian music, adding accordions to the traditional fiddle sounds and a heavy backbeat that comes from African and Native American sources.
It is worth reiterating that the traditional geographic heart of Cajun culture is not in New Orleans, but rather in rural South Louisiana. Certainly plenty of people of Cajun descent live in New Orleans now, but it is not the hub of Cajun culture by any stretch, and Cajun restaurants and musicians are, generally speaking, an import to the city, not a traditional part of the city's fabric.
So What is Creole?
"Creole," as a term, is a bit more complicated than "Cajun," in that it has multiple definitions. A whole lot of multiple definitions, actually.
The simplest and shortest (but probably least relevant) definition of "Creole" is "born in the colonies." In early sources from the Louisiana colony, you'd see references to Creole horses (considered stronger because they were born and raised in the Louisiana heat), for example.
Creole tomatoes were developed in the early 1900s as a hardy variety that grew well in the Louisiana heat.
But Creole came to refer to people of European descent who were born in the French and Spanish colonies, and later often implied people of mixed European and African (and occasionally Native American) descent. At this point, both of these definitions are still true. You'll hear references to "white Creoles" or "old-line Creole families," which indicates direct descendants of original French settlers to the city. When food is referred to as Creole, it is usually the traditional gourmet food of this wealthy community, but it's worth remembering that this food was generally developed by enslaved women working in their kitchens, so it has multiple influences (think French mother sauces with African and New World ingredients, like okra and filé).
Creole is also a term of identification for people of color of mixed African and European descent, again largely from families who have been in Louisiana since colonial days. Whole books have been written about the complexities of race relations in New Orleans, which have been intricate and largely impenetrable for the entire history of the colony, but suffice it to say that folks who self-identify as Creoles do have a different identity than folks who self-identify as black. (And to confuse things further, plenty of people identify as both, and certainly outsiders have no real way of knowing the difference, the latter complexity being a major facet of the famous Plessy vs. Ferguson case.) Short answer: if you're not from here, you might never understand. And that's okay.
To complicate things further, most people of color in the Cajun regions of Louisiana (which is to say, most of South Louisiana outside of New Orleans and Baton Rouge, but particularly around Lafayette and Lake Charles) self-identify as Creole, even if they have only minimal European ancestry. Creole in Cajun Country simply means "historically francophone African-American." It is these rural Creoles who created zydeco music and who are known for Creole cowboy culture, which includes trail rides and cowboy clubs that exist to this day. Creole food is similar to Cajun food, but tends to be a bit spicier (though with everything on this topic, there are plenty of chefs from both styles who will break that rule).
To confuse things further, many of these rural black Creole folks have urbanized as well, but largely in the oil boom cities of Lafayette, Lake Charles, Beaumont, and Houston, which is where zydeco pioneer Clifton Chenier was living when he made the records that gave the genre its name. But don't mistake that culture for the aforementioned Creoles of Color from New Orleans -- they are widespread branches of the same family tree. The former syncretized disparate genres to create zydeco, and the latter did the same but came out with jazz. Still confused? Well. It ain't easy.
Ready for a final bit of confusion? Because Louisiana was historically Francophone, it attracted disproportionate numbers of French settlers up to and including the present day. Some Francophone-descended folks in Louisiana come from these more recent (meaning non-colonial-era) settlers, and consider themselves neither Cajun nor Creole, but simply French, or, in local parlance, French-French.
The Short Answer:
If you're in New Orleans, Creole means fancy and Cajun means rustic. If you're in Acadiana (Cajun country), Creole means black and Cajun means white. This oversimplifies things dramatically, but offers a solid structural framework for understanding these concepts. Either way, if you're in South Louisiana and you hear of a really good Cajun or Creole restaurant, you're very probably safe in assuming that the food is going to be delicious.