I won't go into a great deal of detail as you are a new member and I don't konw your qualifications.
Basically, an Expansion Valve is a type of metering device that maintains a constant superheat as per the manufacturers specifications. There is a sensing bulb on it that connects to the powerhead and the powerhead in turn opens and closes a diaphram to regulate and maintain the superheat.
Adjustable Expansion valves are used typically in commercial applications and allows the technicain on site to adjust the superheat to acheive the manufacturers specifications.
There are advantages and disadvantages to the adjustable. Biggest advantage is the expansion valve can be used on any brand system for its rated size. And since most manufacturers have their own superheat specs., it can easily be adjusted to reflect that. Biggest disadvantage is if the technician does not know its an adjustabe of if the technician is not familiar with how to adjust them, problems could be encountered.
In refrigeration the term "automatic expansion valve" normally refers to a valve used to maintain a constant outlet pressure such as an evaporator pressure requlator. The stem in this case would be the pressure setting.