Three names for one animal, and a map hiding behind them
Crawfish, crayfish and crawdad all name the same freshwater crustacean, and all three are correct. Which one you use depends overwhelmingly on where you grew up. Crawfish dominates in Louisiana and much of the South, where the animal is boiled by the sackful. Crayfish is common in the North and in scientific and textbook usage. Crawdad runs through the middle of the country and the West. Some people use two of them, depending on whether they are eating the animal or catching it in a creek.
Dialect surveys of American English have mapped this question for years, and it remains one of the clearest regional divides in the country's vocabulary.
None of them is a fish
The word has a story of its own. It comes from Old French crevice (modern French écrevisse), itself borrowed from a Germanic word related to crab. Middle English speakers borrowed it as something like crevis, which meant nothing to them. So they did what speakers always do with an opaque word: they made it sound like words they knew. The second syllable became fish, because the animal lives in water.
That process is called folk etymology, and crayfish is a textbook example. The "fish" was never there in the original; it was added because it seemed to make sense. Crawfish took the remodeling one step further, swapping the first syllable for craw, as if the animal were named for crawling.
Where "crawdad" came from
Crawdad is the most American of the three. It appears to be a playful variant built on the same craw- base; where exactly the -dad came from is not known. It belongs to the vocabulary of childhood — the animal you caught under a rock with a bent wire — which may be why people who say crawdad defend it with such affection.
There are other local names too. Mudbug is common in Louisiana alongside crawfish, and older regional words survive in pockets. But the big three cover most of the country.
Food word or nature word?
The split is not only geographic. The animal's role in daily life shapes its name. Where it is a staple food, with festivals and boils and restaurant menus, crawfish wins almost everywhere. Where it is mainly something children find in a stream, crawdad holds on. Crayfish, meanwhile, is the word of encyclopedias and biology classes, which is why many people who say something else at home will write crayfish.
Vote for the word you actually say out loud. The tally will help show whether the old boundaries still hold.
Sources: Harvard Dialect Survey (Bert Vaux) and the maps derived from it; etymology of "crayfish" from Old French crevice per standard etymological dictionaries; Merriam-Webster entries for "crawfish," "crayfish" and "crawdad."