"Nuoc" simply means water. There are many kinds of "mam" - which is anything salted and fermented.

Nuoc mam is most often served on the table in a diluted form. Garlic, sugar, chilies, carrots, lime or lemon juice are commonly added. The resultant condiment is something that tickles many parts of your palate. You have something salty/sweet/sour/ and spicy hot as well as fishy. Exactly how this is done varies greatly from region to region in Vietnam.

#1 is the correct way to make nuoc mam. The leftover anchovies can be used as mam after the extraction.