Combs,

Hi! There are 7 types to my knowledge. To help answer your question, I have attached some links with pictures for you to see. Sometimes a picture is easier to understand than some of the descriptions.

http://www.freewebs.com/professorchickenscolours/combtypes.htm
http://library.thinkquest.org/05aug/00044/id16.htm
https://www.backyardchickens.com/web/viewblog.php?id=9280
http://www.animalcorner.co.uk/farm/chickens/chicken_anatomy.html

 

Buttercup
This comb consists of a single leader from base of beak to a cup-shaped crown set firmly on the center of the skull and completely surmounted by a circle of regular points. The cavity within the circle of points should be deep, the texture of the comb should be fine. Also referred to as a cup comb.

Pea
The Pea comb is a medium length, low comb, the top of which is marked with three low lengthwise ridges, the center one is slightly higher that the outer ones. The outer ones are either undulated or marked with small rounded serrations. This style comb has many variations that are still referred to as a pea comb.

Rose
A broad comb, nearly flat on top, covered with regular points, and finished with a spike or leader. It varies in length, width, and carriage according to breed.

Single
This comb is a moderately thin, fleshy formation of smooth soft surface texture, firmly attached from the beak along the top of the skull with a strong base. The top portion shows five or six rather deep serrations or distinct points, the middle points being higher than the anterior or posterior, forming a semi-oval when viewed from the side.

Strawberry
A low comb that is set well-forward. The shape and surface resemble the outer part of half a strawberry, with the large end nearest the beak of the chicken.

V-Shaped
This comb is defined by the two horn like sections that are joined at their base

Walnut
A comb that resembles one half of a walnut meat in appearance.

Above information from Ultimatefowl Wiki