To start and without being fussy, does Type = Strain?
What are the physical differences between the different types?
How can the different types be identified?
What are the different traits between the different types?
What do different types of CAS excel in over the other?
Perhaps, it might be easier, as a starting point, to classifying CAS according to their terrain: Mountain Type, Steppe Type and Desert Type - And build up from there ..
Type = Strain - Yes this is loosely used to mean the same thing though in some cases a type is an established subset of a population. The Mountain Type - would be a good description, not mountain strain. A breeder can produce a strain from that type - say a particular coloring or maybe a lighter boned strain. It is good to find out how the terms are used before deciding on the relevant meaning. In my case, I use type to be established and recognized and strain to be a particular variant of the type.
Physical Difference - are mainly the three that you mentioned and have to do with morphology. Mountain types are usually heavier boned and greater mass on the body. Longer coated with a double coat, heavier blockier heads, deep wide chest, and large paws - all adopted to moving on the mountain and snow. Steppe are not as heavily built have the body type that is between the plains type and the mountain type. Of course, this is dictated by habitat and function. Look for lighter-colored, narrower dogs that can traverse the large expanses of land quickly and efficiently. Longer legged, slightly longer blocky muzzle deep-chested, well tucked up and powerful well-coupled structure. Plains version (desert type) by necessity are slightly built animals with long legs, deep chest, strong lithe muscles, and narrower heads compared to the mountain type. Colors would range more to fawn, straw and multi-colored including a good dose of white. Have a look at some photos here.
You will see many Turkmen Alabai and other types. Some look like Caucasians with docked tails - possibly mountain type and some may resemble the Kangal or Anatolian but with different coloring.
This one is Russian:
Have a look at Murat that was used as a fighting dog - http://sicard.net/gallery/displayimage.php?pid=1051
This one is a Russian import to Israel.
Temperament is a function of breeding and work. it takes about three generations to completely change the temperament in a breeding kennel. The tasks that the dogs is bred for will dictate their temperament. Will continue the discussion later - Christmas calls. :)