Fish sauce is added to soups, to dishes during cooking as well as at the end. Dressing a papaya salad with a fish sauce heavy dressing is only one way of using it, we use it to make dipping sauces.
We also use Anchovy paste as an ingredient in other dipping sauces, and dressings for salads. And we add it to meat dishes much as worcestershire sauce is: given its an ingredient along with Tamarind, it's much the same thing.
In Britain, it's a posh paste to spread on toast, much as we use Vegemite or Marmite. Anchovy toast was an afternoon tea thing.
I think, it's pretty sauce like. If not, I think it's a fundamental ingredient of sauces people reach over to use directly.