I think you need to interpret the SDI Training letter as meaning: "...includes CERTIFICATION of Advanced Open Water or Advanced Diver..." That is, the slash mark is being used as an "or" and "Open Water" is on one side of the "or" and "Diver" is on the other side. They are saying you can have an AOW certification or an Advanced Diver certification, or whatever the various agencies want to call their course that is like those courses.
I understand that. My point is that, looking at the website, SDI does NOT have an Advanced Open Water certification. They have Advanced Adventure Diver and Advanced Scuba Diver Development Program.
So, when an official at SDI sends out something that says "CERTIFICATION of Advanced Open Water/Diver", I think it is extremely sloppy, unprofessional, and just increases confusion for anyone who didn't already know the answer (and thus, wouldn't have been asking the question in the first place). They don't have AOW, and Advanced Diver is ambiguous because it could mean Advanced Adventure Diver or Advanced Scuba Diver.
And what's worse is that everyone seems to recognize that Advanced Adventure Diver is the equivalent of PADI AOW. And it SEEMS like when people are talking about SDI and they say AOW, they really mean, essentially Advanced Adventure Diver. Yet, on the Advanced Scuba Diver Development Program page, down towards the bottom, it actually says:
After the previous requirements are met and verified by an instructor, the instructor issues the SDI Advanced Open Water Diver certification
And if that is actually correct, then things are even worse because PADI AOW is (like SDI AAD) minimal training and experience. SDI AOW being the same as Advanced Scuba Diver would mean that SDI AOW is way more "advanced" than PADI AOW, thus anytime anyone ever says AOW without specifying the agency, it would be totally unclear regarding how much training and experience is implied.
This is the SDI forum. So, even those of you here who continue to use, either, AOW, or "Advanced Diver", instead of being clear and saying, either, "Advanced Adventure Diver", or "Advanced Scuba Diver" are also just contributing to the confusion. If this were the PADI forum, where they have AOW and NO OTHER cert with Advanced in the name (I think? Heck, they don't even have Advanced Buoyancy Control, like SDI does. PADI has Peak Buoyancy Performance, or something like that), it would not be an issue.