Petty knife- The same as a western paring or vegetable knife used when the Chef's knife is just too big for the job. There are some jobs where a smaller blade is called for - Peeling fruit, segmenting an orange, carving meat off a small chicken all involve a more delicate touch which you could do with a Chef's knife but it's just much nicer and safer to do with a smaller blade.
Gyuto knife- The Japanese Chef's knife - Gyuto's vary widely in design but generally range from 210mm to 270mm in length. Tall at the heel, a reasonably flat profile and a gradually curved blade lending itself to an effective rocking motion on the board. For most users a Gyuto is practically the only knife needed in the kitchen.
Santoku knife- Typically smaller than a Gyuto and more versatile. Roughly translated as "three uses" relating to its three main uses; slicing, dicing and mincing. You don't use it with a rocking action Instead it's more of a chopping/slicing motion. Many Western cooks (including me) are now replacing there traditional Chef knives with a Santoku.
Nakiri/Usuba - Thin and sharp, like most Japanese knives, the flat cutting edge and square cut tip make this perfect for chopping and dicing vegetables. The wider squared blade is often used to help scoop and transfer your chopped vegetables to the pot. The Usuba has a more curved blade
Sashimi/Yanagiba - Traditional style Japanese slicing knives that typically have a face sharpened edge, meaning they are sharpened mostly on one side for a much sharper cutting edge. Sashimi knives are used primarily by Sushi chefs to thinly slice fish but the knife is increasingly popular with western cooks for a multitude of tasks including roast carving.
Deba - Traditionally used in Japan for filleting fish but equally suited to boning joints, parting out poultry or for use as a vegetable cleaver. Most Debas are single bevel like the Sashimi ideal for slicing softer, thinner products like fish.