SSI AOW is SSI open water plus 4 full specialty courses, such as deep, navigation, night, Nitrox, wreck, etc.
SSI Advanced Open Water Diver is the next recognition rating on the path to becoming an SSI Master Diver, and includes four SSI Specialty program Digital Kits. After completing the four SSI Specialty programs that interest you, as well as 24 logged dives, you will automatically receive the SSI Advanced Open Water Diver recognition rating, along with your SSI Specialty program certifications.
If you add Stress and Rescue to that you get Master Diver, eg the specialties can be anything, but Stress & Rescue (which requires a current First Aid and CPR to complete the course) is REQUIRED.
SSI AA (Advanced Adventurer) is open water plus one dive from each of 4 specialties, it's not the same as SSI AOW. IT seems to be a gateway to help people decide which specialities they might want to take to completion.
This program allows you to experience five different open water dives from five SSI Specialty programs without requiring you to complete the entire Specialty. If you are unsure of your next step, this is the perfect way to advance your dive skills and experience, and to identify which Specialty programs interest you. You will earn the SSI Advanced Adventurer certification after completing this program.