Oh, this dish. It used to confuse me when I first came to the U.S. and ate at a Thai restaurant for the first time. In ordering "yellow curry," I thought I was going to get one dish only to be presented with another. This is because nobody in Thailand calls this "yellow curry," and what we do call "yellow curry" is something entirely different. I quickly learned from this mistake.
(I was just thinking about this when I took a couple of friends who were visiting from Thailand to a Thai restaurant in Chicago several weeks ago. Unfamiliar with the US Thai restaurant terminology, they, too, were a bit confused.)
If your local Thai restaurant has opted for the designation, "kaeng kari," instead of the more common, "yellow curry," you know that both are the same dish (in the American context, that is). And if some restaurants have two dishes on their menu, both of which go by "yellow curry," pay attention to the descriptions.
When you buy the curry paste needed to make this recipe, make sure you don't end up getting the paste for the other kind of yellow curry. The two are neither similar nor interchangeable. And if Kaeng Kari is what you set out to make, using the wrong "yellow curry" paste will result in a sad, sad situation. I'll talk more about this in the actual recipe.
Kaeng Kari, as I much prefer to call this dish, is one of the milder Thai curries. It contains more of the dried spices typical of South Asian or Middle Eastern cuisines (e.g. Massaman curry) than the fresh and/or dried chilies that are typical of more traditional Thai curries (e.g. red curry). Most Thai kids love this curry as it's not hot at all.
To complement this curry, Thai people often serve a simple cucumber relish (ajat) on the side to add a little zing to a curry that, though delicious all on its own, intrinsically lacks the bold, herbal, spicy ingredients found in other curries. Thai restaurants overseas usually skip the relish, so if you're okay with serving this curry with no cucumber salad, that's fine as well. I personally find that the cucumber relish makes this curry exponentially better.