In western cuisines, we use dairy products like cream to round the flavors and add creaminess to the dish. Coconut milk is the ingredient to do the same in Thai cuisine. Coconut milk (or cream) also helps to tolerate the heat. A more recent variation of Tom Yam Nam Khon (Thai: ต้มยำน้ำข้น) has a little bit of cow or coconut milk added to the broth as a finishing touch. Note that Tom Yam Nam Khon is often confused with Tom Kha Thale, which is galangal (Kha) soup where the flavor of galangal is dominant. While the first soup uses coconut milk just as a finishing touch, Tom Kha is based on coconut milk.
The original recipe is influenced by Lao cuisine. For this hot and sour soup, chicken is the main ingredient, and its original name is Tom (soup) Kha (galangal) Gai (chicken). Thale means an assortment of seafood.
http://www.thaifoodandtravel.com: Coconut Seafood Soup with Galangal — Dtom Kah Talay (or Tom Kha Talay) As it often happens, different authors use different transliterations to English.
I cook my Tom Kha Thale slightly differently. The result is a kind of Thai-flavored bouillabaisse. To rephrase Julia Child’s words: to me, the telling flavor of Tom Kha Thale comes from two things: the Thai soup base — coconut milk, galangal, lemongrass, kaffir lime leaves, fish sauce, lime juice, Thai green chilies — and, of course, the best seafood medley I can get.
I omit mushrooms and prefer shrimp or fish stock instead of water. First, I infuse the cooking liquid with fragrant Thai ingredients. Then I add coconut milk. In this liquid, I simmer different types of seafood, making sure each one stays plump and juicy. The dish is a variety of seafood with intensely flavored coconut Thai sauce. Add some Thai rice or noodles on the side.