I’m a PADI AOW and EANx Diver, so I will be speaking in term of PADI’s Certification.
When you are getting certified AOW, you are supposed to pick 5 specialty dives with Deep and Underwater Navigation as the mandatory dives. For my example, I did Deep, UW Nav, UW Photo, Drift, and Fish ID for the 5 dives during my AOW certification. If you do want to get a specialty in those or any of the other areas, they are totally different, separate from your AOW dives. And for my EANx specialty, I had a class and 2 OW dives for it, again separate from AOW.
Finally, I believe those 5 does not count into any specialties that you might want. Which mean you don’t have 5 specialties by the end of those 5 dives or when you get your AOW certification. You are now just AOW diver with experience in those types of diving.
Anyway, hopefully I’m not rambling here.