OP, I'll try to clear up some of the confusion, at least for PADI.
PADI has three main recreational *certification levels,* OW-AOW-Rescue, each being approximately the prereq for the next. There is an additional certification level - Master Scuba Diver - that is the top level offered; I'll describe it in a moment.
In addition to these certification levels, there are a large number of specialties, each having its own prerequisites. Examples are Navigation, Deep, Night, Nitrox, Search and Recovery, etc. The value and difficulty of these vary depending on your interests, background, experience, etc. They all require 2-4 dives. In general, the first dive of each specialty course is called an Adventure Dive, and is the introduction to the full course.
NOTE: there is no AOW (or Adventure Diver) "class." There is a formal class for OW, and for Rescue, but not AOW. It is just the five separate dives, each with a Knowledge Review. They can therefore be done over an extended period. Normally, a "class" must be completed within 12 months.
There are also Distinctive Specialities written by an individual instructor, approved but not offered by PADI; examples are Coral Identification, Zen Buoyancy, Aquarium Diver, Underwater Basket Weaving, Shore Diving, and Zombie Diver. The value and difficulty of these vary tremendously, from pretty silly to seriously difficult and high value. None of them are valid as Adventure Dives, and therefore not for AOW.
An Adventure Diver certification level means the completion of any three Adventure Dives.
An AOW certification means the completion of five Adventure dives, two of which must be Deep and Nav, i.e. the first dive of those two specialties.
One quirk: Adventure Diver certification, one of the dives being Nav, is the prerequisite for Rescue.
This means if you take five full specialties, two of them being Deep and Nav, then you have satisfied the requirements for AOW....because you'll have done the first (Adventure) dive of each specialty. This also means you learn much more....five full specialties instead of just an intro to each. But this does not mean you automatically get your AOW certification level card.....you still have to pay for that, because it is a separate card....but should not cost more than $30-35 dollars, maybe less if you cut a deal with your shop/instructor..."Hey, I'll take five specialties from you and you throw in the AOW card!"
Once you have AOW, Rescue, 50 logged dives, and five full specialties, you can apply for Master Scuba Diver. What is this good for? Personal pride, and occasionally a better seat on a dive boat.
Another quirk: the five specialties for MSD can include Distinctive Specialties.
If you were to move into the professional ranks, starting with Divemaster, you need AOW and Rescue, or their equivalents from some other agency.
Suggestion: if you find a good instructor, talk it over with him/her. If they seem narrow-minded or inflexible, find another instructor. You'll also probably find that the instructor who can give you an outstanding Peak Performance Buoyancy class may not be the same one who can give you an outstanding Search and Recovery class, or Rescue class, or Underwater Naturalist class, or Digital Underwater Photographer class. Shop around. Be skeptical. Interview them.
Good luck. Don't hold your breath, have fun.