As far as I’ve known, we (as Thais) have two types of Tom Yam (Spicy Thai soup) which are ‘dense soup’ (Nam Kon) and ‘clear soup’ (Nam Sai). The difference of those types are that the one with dense soup has chili paste and plain milk, which this type is not the original one but it has adapted from the ‘clear soup’ type by adding plain milk during 1910-1925 by Chinese restaurant in Thailand (Source).
The main same ingredients for those types are galanga, lemongrass, kaffir lime leaves, Thai chili, lime, and Thai fish sauce. Besides shrimp or prawn that can be used as meat for Tom Yum, we can use seafood like squid, fish and shell. For vegetable, we like to put mushroom which can be Rice straw mushroom (Hed Fang) or Sajor-caju Mushroom (we call Hed Nang Fah in Thai which means Angel mushroom).
Tom Yam Kung Nam Kon (Spicy Thai dense soup with shrimp)
1. Boil water with any stock (my family uses Fish stock that we bought in Japan, it comes as dried powder) and put the 3 main ingredients galanga, lemongrass, and kaffir lime leaves.
2. After the soup is boiled, drop shrimp/prawn into it.
3. When shrimp’s color turns to be orange, pour plain milk and chili paste. Seasoning it with smashed Thai chili, Thai fish sauce, and lime squeezed. Then, put mushroom into the soup.
4. When everything is cooked, showering it with chopped celery and coriander.
And it’s done.