Active and dormant are part of the yeast cycle and has nothing to do with sales or packaging.
Yeast becomes active when it detects that is in a nutritious environment. Then it starts fermenting. When all nutrients (sugars) have been used up, then the yeast becomes dormant, and then it flocculates out of the solution.
When it is liquid dormant, it can be dried, and then you get dry yeast. Liquid packages of yeast are also dormant.
I have at home trappist yeasts in liquid form in my fridge, these are all dormant.
I think "Dry Active Yeast" has more to do with marketing than technical merits. I even found a reference saying "active dry yeast is a dormant yeast". But apparently this term is more used for baking yeast.
Rehydrating or not, some producers recommend it, and others don't. That is more to make the life of the hobby homebrewer simpler. I won't go into the pros or cons, because it is still being debated to death every now and then on most homebrew forums.
Answers to followup questions:
a) All dry yeasts can be hydrated or pitched dry. What is being debated is if it makes a difference in:
- quality of the beer
- viability of the yeast
b) Yes, dry yeast stores better than liquid yeast. Viability of liquid yeast drops quickly. I have used dry yeast of more than two years old, stored in the fridge, without problems. I have used baking yeast of five years old, stored in the fridge, without problems for making bread.
c) Yes, there are less beer yeasts available in dry form, than liquid yeasts. However, (small) commercial brewing will probably use a dry yeast that best fits their product. It is much cheaper than buying liquid yeast, and one doesn't need laboratory equipment to create starters. And liquid starters tend to grow big, which means investing in laboratory material, making wort for starters, time to grow starters etc...