Steve almost has it completely well-put. PADI’s Advanced Open Water (AOW) is 5 "experience" dives to include Deep, Navigation and 3 Diver’s choice experiences. SDI’s Advanced Open Water is only available once you have completed 5 full specialty certifications (usually 4 training dives per specialty) and a minimum of 25 dives. With PADI you can be AOW after 9 total dives (4 OW and 5 AOW) but with SDI it’s 25 (4 OW, 4x5 Specialty and 1 additional dive - training or non-training). So one could argue that an SDI AOW certification is bestowed upon a more trained diver. SDI does have the "Advanced Adventure Diver" certification to compete with PADI in the business driven marketplace of short attention spans. This is 5 experience dives that can later be credited toward your AOW certification but the AAD is the same as PADI’s AOW.