Nước chấm literally means "dipping sauce" and so it includes all kinds of sauces used for dipping. Each dish usually accompanies a specific flavor of dipping sauce, and there can be heated debates as to which dipping sauce is the most appropriate for a particular dish. That said, nước chấm at any restaurant is generically understood to be the house flavor of nước mắm dipping sauce, which is essentially their take on the ratio of nước mắm, water, lime juice/vinegar/pineapple juice, sugar, and chili. As you travel from North to South, this dipping sauce becomes sweeter (with an exception for the Huế area, where you'd find even their basic level of spiciness scorching hot if you're not used to eating spicy food).
