What is the difference between Alaskan King Salmon and Scottish Salmon?
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.