The coif is a word that refers to a couple of different things that cover the head. It is usually not a specific hairstyle, but a plethora of styles, and it could also be a type of cap. It is close fitting and covers the top, back, and sides of the head.
A popular use of the coif is to be able to distinguish between judges. They were, at one time, a standard headdress for judges in the medieval time, specifically for serjeant at law. They were forced to wear the cap all the time, even in the presence of the king. However, they covered it with a black cap when they were giving out the death sentence.
Quaff, on the other hand, typically means to drink or guzzle down an alcoholic beverage enthusiastically. It may mean drinking large amounts or ingesting a large quantity at one time; however, it could also mean quaffed hair. Quaffed hair refers to hair that has just been freshly styled or using a lot of hairsprays.