Wool:  This word has become a loose definition for hair that has been sheared from an animal.  Wool is most commonly harvested from sheep, although may also be taken from goats or even camel.  

Dead Wool: It's brittle, coarse, poor quality wool used in production of many high volume, commercially available rugs (Fast Food).  This type of wool often will shed profusely, and render a rug lifeless in a short period of time.  Dead wool is often the refuse from combing out finer, longer stapled wool.

New Zealand Wool: Typically New Zealand wool is often known for it's longer staple, and naturally soft feel (Fine Dining).  This is due in part to both the altitude and vegetation available to herds.  It's not uncommon for a rug to have a New Zealand and local wool blend to counteract the investment of import and material cost.  

Gazni Wool: Typically found in higher quality peshawar weavings, this comes from high grazing sheep in the mountains of Afghanistan.  This wool is soft yet firm to the touch: Depending on the way in which the wool has been treated, Gazni wool often has very slippery (almost oily sides), with a crisp and strong feel after clipping of the pile.

Semi-Worsted Wool:  Semi-Worsted wool is a very solid quality wool which is retrieved from wool by the process of combing.  After wool has been combed, finer, longer strands of wool are separated from shorter less desirable wool.  The term Semi-Worsted wool refers to a wool which has been produced by one of two ways: Either the very high grade wool (after being separated from low to mid grade), or the highest grade wool which is separated from the lowest grade and then is blended with a medium grade wool.

Worsted Wool: Worsted wool refers to a process (and product) of combing excellent quality wool from high, medium and lower grade (determined by length, or staple.)  After wool has been combed, the finest, longer strands of wool are "Worsted." 

Qurk / Kork Wool:  Qurk wool is taken from the neck, belly and underarms of the sheep.  This is often considered the most choice of wool to come from the sheep, as it is very fine, thin, and long stapled.  Kork wool is most often reserved for only the finest of weavings.  Perhaps this type of wool is most commonly found in high-end oriental rugs.  The appearance of fairly untreated Qurk wool has almost a dull finish, yet very compact, firm and dense feeling pile.

Pashmina Wool:  Pashmina wool is exclusively taken from the coat of Himilayan goats.  This wool is very silky, long stapled, and very unusual to come across in exported weavings from rug producing countries.  Pashmina wool is very soft, highly sought after, and very expensive. 

Mohair: Mohair is harvested from the Angora Goat.  Mohair is often very fine, long stapled and have a silk like appearance and feel.  Mohair rugs are very unusual to come by, as mohair is a very expensive and hard to come by fiber to be used in production of Oriental Rugs.  One should carefully inspect a mohair rug for color run, as it's not entirely uncommon to find overdyeing of colors which could potentially run. Also, be careful when purchasing mohair, most find out later that they are allergic. If you can manage getting a sample, I highly recommend it. 

Chemically Washed Wool Rugs:  There are techniques which are used post production which chemically treat the wool pile of a rug to give it a softer feel and more lusterous pile sheen.  While these washes may be used successfully with little affect to the woolen fibers, it is not entirely uncommon to come across a rug which has been too harshly treated with this process.  Similarly, there are rugs which have a very low quality wool which have been subjected to these washings which make them appear to have a better quality wool than is actually used.  In both cases of too harsh a wash, or low quality wool to begin with, copious amounts of shedding will be apparent from the aggitation test.