I'm considering throwing a dinner party, and I don't have much experience cooking salmon. What are the main differences between these two types of salmon in terms of price, taste, and cooking methods?
Alaskan King, or Chinook, salmon is generally wild, generally caught in the Pacific Northwest, often but not exclusively in Alaska. Scottish salmon is generally farm-raised Atlantic salmon, and as far as that goes is essentially identical to farm-raised salmon from Chile or Norway.
Price: hobodave's comment is correct that the price will vary based on location, but in fact the king salmon will be more expensive almost everywhere. Generic farmed Scottish salmon is a commodity product that generally sells for about $1 more than other farmed salmon for no particularly good reason, but wild salmon can easily cost twice as much regardless. Short of actually being in the Pacific Northwest it's likely that the Scottish is substantially cheaper.
Taste: the quality comparison is the big one here rather than species. King is usually treated much better (shipped quicker, wild diet) because it's not a commodity, but not necessarily. Scottish will vary depending on the farmer, but I think you have to prefer the King to any generically-farmed Scottish salmon.
Cooking methods: no necessary difference. Smoked on a plank is a common method in the Pacific Northwest, but no real reason you couldn't do either in that way. Pick your favorite method.
There are five significant species of Pacific salmon, and only one species of Atlantic salmon, which actually runs into the east coast of North America as well as in Europe.
In terms of cooking, the same processes apply to all - you don't have to adjust for the species, the process works similarly.
For taste, wild salmon definitely tastes better, and the Atlantic salmon is mostly farmed, but you can buy wild Scottsh salmon.
There is a substantial industry in wild Scottish salmon, so if you know you are buying that type you are buying the best. Here in the UK Norwegian salmon sells for high prices which it does not warrant, they farm it just like the Scots.
For taste, go for wild Atlantic salmon, then fresh wild Pacific salmon. Beyond those considerations, the farmed stuff is worth having - balance the local price against what you are going to do with it. If you're going for one of those flavor-drowning salmon mousse recipes, a can of Cohoe goes a long way ...
Firstly, I'm British, so I may be biased, but in my experience, farmed Atlantic Salmon tastes just as good as wild. It's certainly cheaper, and they're not exactly farmed intensively like battery chickens.
Speaking from personal preference, my wife would not be happy if I brought Pacific salmon home. I did once, and the flakes were smaller, tighter and less succulent than the Atlantic we normally have. Never again. Curiously, if you buy cheap frozen salmon in the UK, it's Pacific, which has never made sense to me. It would do for a mousse or pie, but for a fillet or whole fish, we find it just too coarse.
In terms of cooking, you can do almost anything, although "gently" would be my keyword. You can marinate it in pretty much any spice/herb marinade, although dill is the classic herb to go with salmon. You can grill (broil) it, steam it, pan-fry it. I prefer to put it in a dish with some fish stock and bake for 15-20 minutes at about 300F (150C), with foil over the top. You can tell it's cooked when the shine has gone off the flesh throughout. Then a dill cream sauce over the top is divine. There are literally so many ways of cooking salmon, I couldn't choose a favourite!
With all due respect to the Brits and Scots (and certainly the Canadians), The Pacific salmon fishery is the largest producer of the best quality salmon. ( The Russian fishery I would consider as Pacific). I have never fished a Scottish Wild Run, I believe most of those fish are taken by the remains of the Aristocracy as sport fish. (read expensive). If you are NOT within 100 miles of the point of origin, the lowest cost salmon is Farmed. Almost all farmed salmon are Atlantic, dyed color or not.
My Father grew up seining on the Columbia River Bar, sometimes when young I helped smoke salmon with local tribes. My mother hated cooking salmon because it "stunk up the house".
Cooking: Most chefs use heavy sauces (egg sauce, creamed dill type sauces) when cooking stronger flavor salmon. Milder pink fleshed, light red color salmon can use any French sauce for trout, simply use Escoffier or Larousse cookbooks. For smoking, the Scots and the Norwegians have techniques on the Internet. The American/Alaskan natives have theirs mostly secret. It is very suitable for outdoor,backyard grilling, oven baked pain with lemon and butter, maybe a bottled Chinese Oyster sauce. Great poached in wine, or poached and served later cold on a salad. Or bake a whole small fish stuffed with crab, shrimp or ? stuffing.