Chicken Rochambeau from Restaurant Antoine, the oldest operating restaurant in New Orleans.
The difference between "Creole" and "Cajun" food is something that confuses both locals and visitors to New Orleans. Here's a brief explanation of the differences.
The very short explanation is that Creole cooking is from the city and Cajun is from the country.
The term "creole" has its own history and controversy. The original "creoles" in New Orleans were the French and Spanish families that founded and grew the city in the 18th century. The French colony of Louisiana dates back to 1699, and Spanish interaction was natural once the port was established. By the 1780s, the French had sold Louisiana to the Spanish, which meant there was an even greater influx of Spaniiards to the city. When the sleight-of-hand deal that resulted in the US acquiring Louisiana took place, many of those Spaniards remained in the city.
It's at this point that there's a true distinction between Creoles and the rest of the world begins, because the Americans coming down from the Mississippi Valley, Tennessee, and Kentucky (the "cain-tocks") were so different from the European residents. The "Creoles" had their side of town, the down-river side of what would become Canal St., and the up-river side, Faubourg Ste. Marie, was the "American" side. Of course, the food of the creoles was much more interesting and tasty than most of what those of English and Irish descent cooked up. By the 1850s, several creole restaurants were becoming very well-known, such as Mme. Begue's, and Antoine Alciatore's place on Rue St. Louis.
Creole cooking is about taking a simple dish and using sauces and gravies to make it fancy. Take the dish in the photo above, Chicken Rochambeau. Place several slices of baked ham on a piece of toast. Cover it with "Rochambeau sauce," which is a beef stock and brown sugar sauce. (Some restaurants use Marchand de Vin sauce for the dish rather than outright copy Antoine's Rochambeau sauce.) Then cover that with severl slices of roasted chicken, or a grilled chicken breast. Top the chicken with Bernaise sauce and serve.
Now, think about the simple elegance of this, along with the practicality. You roast a chicken, and a ham. You can use both in a number of different ways. A family can make several meals out of them, and a restaurant can make a number of totally different dishes by simply serving them with different sauces.
Trout is another good example of how creole cuisine works. Take a nice-sized filet of speckeled trout. You can grill it and serve it with a little butter and/or lemon. Or you can dust it with a little flour and pan-fry it. Take that same pan-fried filet and pour some brown-butter Meuniere sauce over it and you no longer have just fried fish, but Trout Meuniere. Roast some thinly-sliced almonds in the buttery sauce and you have Trout Almondine. If a restaurant's fish guy has a good run on trout for a couple of days, a regular diner could eat trout three days in a row and still be happy about it.
The Italians who moved to New Orleans picked up on this concept fast. We ate this evening at a suburban restaurant, TeCoRo's (short for the names of the three sisters who own the place). They are what we call a "Creole-Italian" restaurant. Their base menu consists of chicken, veal, and eggplant, served with one of three sauces: Plicato, cream, mushrooms, sun-dried tomatoes, and cheese, Piccata, which is lemon butter with capers, or Marinara. Simple to deal with in the kitchen, yet the variations and combinations are wide enough to make things interesting.
That's the essentials of Creole cooking in a nutshell, the simple made elegant.
Cajun food might well be called "peasant" cuisine in another culture. This is country cookin', because Cajuns were essentially just that, country folk. When the Acadiens came to South Louisiana, they didn't have much in common with the city folks, so they settled away from New Orleans. That separation, along with the much simpler life of farming, fishing, and hunting, helped them develop cuisine significantly different from the "cultured" tables of the European colony. Cajun cooking's staples are simple fried foods, soups, and stews. Gumbo and etouffee are good examples of cajun cuisine. Both are essentially single-pot (well, two, if you count the pot for boiling rice) dishes. Fried fish and chicken also are common elements of cajun cooking.
Shrimp versus crawfiish: The distinction is a lot less these days, because of commercial, domestic crawfish farms, but there was a time when creole cuisine was more about shrimp and crab and cajun food was about crawfish. Shrimp and crabs were readily available to the city from Lake Pontchartrain. Crawfish, however, are creatures of the swamp. We don't call them "mudbugs" for nothing! For generations, you couldn't get decent crawfish etouffee in the city--restaurants used shrimp. If you wanted good crawfish dishes, you had to go out to Acadiana and dine at a restaurant in Lafayette or Breaux Bridge.
"Blackened" anything: This type of cooking isn't cajun, strictly speaking. It's Paul Prudhomme's style. While Prudhomme is one of the most well-known cajun chefs, he created his own style and brand, and burning a blackened crust onto redfish or a steak is it. (Interesting side note: Prudhomme was executive chef at Commander's Palace in New Orleans before opening his own place, K-Paul's, in the Quarter. In the early 1980s, he got a huge break when St. Ronald of California invited him to be the chef for a G7 meeting hosted by the US at Williamsburg, VA. This propelled him into the spotlight. Upon leaving Commanders, Prudhomme's lead assistant took over the restaurant, a guy named Emeril.)
How do black folks fit into all of this? Unlike the rest of the south, where there was a huge distinction between "white" cuisine and "soul food," you really didn't see that big divide in New Orleans. That's because black folks did most of the cooking for everyone! The better-off creole families had black house staffs, and black cooks have staffed the better restaurants of the city for generations. There are some establishments (Dooky Chase, or the late, lamented Chez Helene to name two) where there is/was a more distinct black style than, say, an Antoine's or Galatoire's, but the differences are more subtle than glaring.
Cajun and Creole both began to merge and cross over in black households. Red beans and rice is a good example. It's essentially another single-pot dish, but black folks in the city would go beyond the basic ham or andouille sausage of the cajuns and serve fried chicken or pork chops cooked in a more creole style with their beans. It was black families that combined the elegance of creole with the low-budget eating of the country folk.
To say this is all a huge oversimplification is an understatement. I've left out the influences of the Germans, the Irish, Latinos, and Africans that all passed through the port of New Orleans. Still, you get the basic idea--the locals took ideas from all these cultures and mixed in what works for us. The Honduran who worked as a cook in a French Quarter restaurant might show the others on the line something his mama did, for example. Whatever it was might not make the Galatoire's menu, but the black guy who noted that dish/sauce/whatever, might use it when he leaves the Quarter and opened his own place. That's how it works, and that's what keeps our food constantly interesting and changing.