Any decent course will provide an outline describing what that course trains the diver to do. That is often coupled with recommended guidelines setting realistic limits on activities, based upon the training provided.
When it comes to qualification, the general rule is 'dive within the limits of your training and experience'. So... if you weren't specifically trained to do it... then the agencies don't recommend that you do it. Simple yah?
Examples:
PADI OW Diver - Recommended maximum depth of 18m/60ft for newly trained divers. No deco. No overhead environment. Seek further training to dive in conditions that are not similar to what you trained in.
PADI AOW Diver - Recommended maximum depth of 30m/100ft. No deco. No overhead environment. Seek further training to dive in conditions that are not similar to what you trained in.
PADI Deep Diver - Absolute maximum depth of 40m/130ft. No deco. No overhead environment. Seek further training to dive in conditions that are not similar to what you trained in.
PADI Tec40 Diver - Absolute maximum depth of 40m/130ft. No more than 10 minutes deco, calculated on back gas (but >50% O2 can be used). No overhead environment.
PADI Tec50 Diver - Absolute maximum depth of 50m. Unlimited accelerated deco, using up to 100% O2. No overhead environment.
PADI Wreck/Cavern Diver - Penetration within the 'light zone', no restrictions, no more than 40m130ft linear distance from the surface, no deco. This means, you shouldn't go into areas where you aren't illuminated by light from an exit point. You should not go through spaces that are too small for two divers to pass side-by-side whilst sharing air. You exercise dive planning and management to ensure that no-deco limits are maintained. You are never more than 40m travel to the surface.
PADI Technical/Advanced Wreck Diver - No restrictions on depth, deco or penetration. General recommendation to progress penetrations consistently with your experience and capability -based on individual risk assessments.
Cave Diver (various agencies) - Various restrictions on penetration, conditions, equipment and gasses used - all specifically tied to the course/training content and the standards that need to be achieved by the diver on those courses.
The same is true for other agencies.... they set specific limits appropriate to the specific content of their courses.
As for Rec versus Tec.... don't spend too much time trying to find a strict dividing line. At the best, all you will find is an agency specific definition. Some definitions are more popular than others (community consensus), but none are a 'rule'.
Generally 'no-deco' is used in connotation with recreational diving. The principle being that recreational divers should always retain the ability to immediately ascend to the surface if there is a problem. Where overheads are concerned... the use of 'linear' 40m/130ft penetration equates to restricting the same 'time from surface' as that of open water divers.
So, for me... recreational simply means: Can ascend directly to the surface if there is a problem + is never more than 40m/130ft from the surface.
Technical diving exceeds those limits... and because the surface is not immediately accessible (by depth, deco or overhead) then a much more robust system of skills, procedures and equipment considerations needs to be in place to protect the diver and ensure they can reasonably deal with any foreseeable problems without having to surface. Likewise, a much higher degree of core diving skill and robust mindset needs to be confirmed, so that the diver is able to control themselves and will not be subject to accidentally exceeding ascent rates, deco ceilings, max depths... or otherwise causing critical issues (i.e. silting) in overhead environments.
Another term for recreational diving is 'No Stop' diving. Perhaps that is the most basic factor.
