That's quite a few names for the same thing. Below are some recipes for both Cray and Crawfish.
Here's a zoological tidbit about Crayfish:
It is a matter of common information that a number of our streams and rivulets harbour small animals, rarely more than three or four inches long, which are very similar to little lobsters, except that they are usually of a dull, greenish or brownish colour, generally diversified with pale yellow on the under side of the body, and sometimes with red on the limbs. In rare cases, their general hue may be red or blue. These are "crayfishes," and they cannot possibly be mistaken for any other inhabitants of our fresh waters.
Caavpisn (Salad of).*—Boil crayfish as usual, take them from the shells, put them into a salad-howl with anchovies, artichoke hottoms, and seasoned like other salads.
Caavpisn Soup.—Put some eels, flounders, &c. into cold water, set them on the fire, and when near hoiling, skim, and add to it onions, carrots, parsley, and whole pepper. Take ahout fifty crayfish, and having taken them from their shells, put them into the fish hroth, also the small claws and tails, finely pounded; let them hoil for an hour, then strain it off; add some crusts of hread, and the spawn of a lohster pounded.
Caavpisn Soup.—Boil six whitings, and a large eel, with as much water as will just cover them; skim them clean, and put in whole pepper, mace, ginger, parsley, an onion, a little thyme, and three cloves l hoil them to a mash. Pick fifty crayfish, pound the shells, and a small roll, hut first hoil them with a little water, vinegar, salt, and herhs; put this liquor over the shells, on a sieve; then pour the other soup clear from the sediment; chop a lohster, and add this to it, with a quart of good heef gravy; and also the tails of the crayfish, and some flour and hutter, and season according to your taste.
CRAYFISH (Bisque of).—Take ahout fifty or sixty crayfish, stew them in a little water, with carrots, onions, parsley, thyme, hay leaves, salt, and pepper, for half an hour, then drain, and take them out of their shells; and having laid aside thirty of the tails whole, pound the remainder of the meat with the hreasts of two roast fowls, the crumhs of two French rolls, previously soaked in rich hroth, and the yolks of three hard eggs. Boil the shells in a little hroth, and, with the liquor, dilute the pounded meat, and ruh the whole through a silk sieve. lioil a piirt and a half of cream, keep it stirring, and pour on the soup; season it, and add the coral of a lohster pounded, and mixed with a little hroth; set the whole on the fire, hut do not let it hoil. When quite done, pour it into the tureen on some previously soaked hread,
and put the tails which were reserved, on the soup, and serve it hot.
To boil crawfish, make a court bouillon with water, salt, whole pepper, vinegar, parsley, green onions, bay-leaf, and mace; when the water boils throw in the crawfish, let them boil not more than fifteen minutes: they may be served plain in the second course, dished on a napkin.
Ecrevisse a, la Poulet.
Pick out the tails of crawfish that have been boiled as above, trim the thick end of the ragged part, then take two or three spoonsful of bechamel (No. 7), stir it over the fire till it boils, mix in a little chopped parsley, a few drops of lemon juice, throw in the crawfish, thicken the sauce with the yolks of two eggs, and a spoonful of cream. The crawfish may be served in a volau-vent, or a casserole.