Fur, hair and wool - what's it all about?

A human hair
Photo done by Scanning Electron Microscopy (SEM)
© 2010 University of Minnesota Duluth

What's the difference between fur, wool and hair? This is a question that has been bugging me for a long time, so I tried to find out the answer. Let me tell you right up front that I didn't find a simple answer. The following is what I have gleamed but please post a comment if you can add any clarity to this question.
Some of this confusion seems to be a matter of word usage, as they are all the same protein (keratin), so technically they are all hair. However, some features that help distinguish the usage of terms: The thickness for example. Hair has lower density with 500 follicles/sq inch although not all are active at the same time, so let's say @100-200 follicles per sq inch should define hair. Sheep wool on the other hand, have up to 60,000 follicles/sq inch (Merino) and if the density is high, like a sea otter which has one of the highest densities at 800,000 per sq inch, the hair is referred to as fur. 
Another characteristic that some use to distinguish between terms is the growth pattern. Fur grows to a certain length then stops, while wool and hair keeps on growing. Although, this all depends on species and genetics, but generally this seems a good separator. Fur tends to have a major shedding time annually. Only the primitive sheep (eg. Soay, Orkney, Hebridean) and the so called 'hair' sheep breeds (eg.Saint Croix, West African, Wiltshire Horn) shed annually. 

Churro sheep wool. SEM
Photo by Dave Lewis and the Ohio 
 Agriculture Research and Development Center in Wooster

Wool tends to be the term for sheep fleece. Some sheep have kemp (thick hairs) in amongst the wool usually in is found in certain breeds of sheep and certain locations (eg. rear end), other sheep and Llamas have double coats with longer guard-type hairs designed to shed water and shorter insulating down fur (eg. Icelandic, Navajo Churro) for warmth.

Alpaca.
Photo by Dave Lewis and the Ohio 
 Agriculture Research and Development Center in Wooster

And then there is the more technical characteristics, like the cellular structure. The hair shaft is made of cuticle cells (keritine) that form scales, overlapping each other and pointing towards the tip. The cells form a protective coating around the cortex (inner area). In the fine merino wool, the cells are one layer thick while human hair can be 10 layers thick. This cellular structure is different for each type of hair (eg. eyelashes, whiskers, hair) from different animals. The scanning electron microscope photos here show some of the different structures. Look at the difference between human hair, churro sheep and angora rabbit in the pictures here. But, it doesn't help much in distinguishing hair from fur from wool.

Alpaca  Light microscope photo
showing the medulation (dark areas).
Photo by Dave Lewis and the Ohio 
 Agriculture Research and Development Center in Wooster

Inside the hair shaft is the cortex. This is the middle of the hair/wool/fur. If the centre of the cortex is hollow we call the core 'medulla' or a medulated hair. The inner core can be a consistently hollow core, or contain sections which are hollow. This medulation can provide insulation, hence hairs with no medulation hold heat less well than medulated hairs. Alpacas and Llamas have medulated hairs while sheep do not, hence Alpaca wool is a better insulator than wool.

Angora. Note the very interesting V-shape cell structure
SEM Photo by Dave Lewis and the Ohio
 Agriculture Research and Development Center in Wooster

So why is this interesting? For a few reasons. The structure of a fibre creates its characteristics for: heat retention; strength, elasticity, felting tendency, light reflection, etc. And also because I want to be able to analyze a fibre and have a way to figure out if it is Mountain Goat or sheep wool or from the Coast Salish wool dog.