PADI Rescue doesn’t actually have a qualification depth as such, in the same way that OWD qualifies you to 18m and AOWD qualifies you to 30m. Being a Rescue Diver is about expanding your diving awareness outwards beyond yourself, towards your buddy and other divers, and learning to recognise developing problems and solve them before they turn into a serious incident. That’s why it’s a prerequisite for the PADI Divemaster rating
The course syllabus itself actually contains very little time underwater: the only underwater drills are ‘distressed diver underwater’, ‘underwater search patterns’, and ‘surfacing an unconscious diver’. The rest of the course components are surface-based training, although you will likely also do a couple of simulated open-water rescue scenarios to conclude.
If you want a PADI card that increases your depth qualification limit, then the Deep Diver Specialty is the one to go for, which increases your training limit to 40 m. However, due to the laws of physics, and the fact that PADI teaches ‘recreational’ (i.e. no-stop) diving only, being able to dive to 40m as a ‘recreational’ diver isn’t all that useful.
This is because the no-stop time limits–which include your descent time, don’t forget–at these depths are very short (e.g. 9 mins @ 40m on the PADI Recreational Dive Planner). For e.g. a wreckdive at 35-40m on a flat seabed, you’ll have only about 5-10 mins on the bottom, before you have to ascend, and will be in the water for about 15-20 mins total, including your descent/ascent and ‘safety-stop’. Unless you can do a multi-level profile, e.g. on a reef wall, 40m no-stop dives become hardly worth doing. For worthwhile bottom times at anything deeper than about 30 m, you really need to think about getting trained in ‘technical’ (decompression) diving, as another Answerer has already said.
PADI’s affiliate company DSAT now offers tech-diving courses (the ‘TecRec’ program). The entry requirements for the ‘basic’ course (DSAT TecDeep) are pretty high as far as I recall. In order to enrol, you must already hold PADI Deep Diver and EANx Diver Specialties (or their equivalents), and have a certain number of logged dives (can’t remember exactly, but at least 50), of which a somewhat smaller no. must be to 30m+ and/or using Nitrox.
An alternative route to tech-diving qualification is the system offered by TDI:
Basic Nitrox teaches ‘recreational’ EANx use (up to 40% O2)
Decompression Procedures teaches general deco-dive planning/equipment/techniques to max. 45m
Advanced Nitrox teaches ascent planning using rich (40-100%) nitrox to reduce stop times (Basic Nitrox is a prerequisite)
Extended Range teaches deco-planning to 55m, using air and nitrox–(Deco Proc and Adv Nitrox are prerequisites)
The final qualification (Extended Range) is effectively equivalent to the DSAT TecDeep (50m using air, nitrox and 100% O2), both in terms of theory and total no. of dives required for certification. However, the entry prerequisites for the TDI courses are not as stringent as for TecDeep, and the individual courses are shorter, allowing the student to absorb and practise the information/techniques in smaller chunks, over a longer period, and according to their specific interests.
TDI instructors also have a little more flexibility in how they teach the courses than DSAT instructors, which means that course quality is very much more dependent on the instructor’s own attitude to teaching. TDI courses offer a ‘toolbox’ approach to deco-dive planning/equipment configuration, and concentrate more on making a diver completely self-reliant, whereas the techniques/equipment configuration taught by DSAT are basically DIR by another name, i.e. more prescriptive and ‘team-oriented’.