Many sources use "recreational" to describe diving with ordinary air (or maybe nitrox), and "technical" any diving with more complicated requirements. Both are distinguished from "professional" diving, so you can be doing "technical" diving recreationally without doing "recreational diving".
Wikipedia says that the exact definition of "technical" varies between certifying agencies, but 50 meters is definitely well below it. You can certainly do it without being certified, but the training classes make it clear that you're taking a massive risk (oxygen toxicity, nitrogen narcosis, decompression sickness).
I've got only the most basic certification myself, and only a short list of dives, so I can't speak to how realistic that is.
I’m not sure where you’ve been diving or if youre intentionally being pedantic.
Your typical open water course qualifies you for depths to 30m. I’ve been past 40m, but on air you’re not staying there very long (let alone 50m). And if I remember my nitrox training correctly, on EAN 35 you want to stay at 30ish meters or shallower.
My insurance through DAN also only covers me for up to 30m. Most of the colourful corals and fish that you see on TV, typically at shallower depths anyway.
Past 30m you definitely need further qualifications and more gear if you want to hang out at those depths.
First off, I'm not diving in the US and I'm not well-versed in how insurance/rules are there.
Secondly, yes. You should have proper training and experience. And that's why I said 'experienced' divers. I wouldn't count myself among them with my less than 50 dives and lack of qualifications.
However I personally know quite a few experienced divers (most of them have >1k dives total) who do this kind of thing a few times a year. Usually to spend a few minutes looking at wrecks.
Granted, I am positively surrounded by people with way more experience than myself so I may have a skewed image of what is normal.
I’m not in the US either. I’ve clocked at least 100 dives. I stopped counting at 70. I assume you’re somewhat familiar with the conditions of your insurance. If you’re diving regularly without insurance, I’d suggest you go get some.
Doing wreck dives at 60m is not like recreational diving. Different air mix to get those depths and stay for any significant period. The guys I’ve talked to, leave extra tanks at the half way point for deco. Otherwise you won’t have enough air.
Compared to ‘recreational’ diving: call up your buddy, check conditions, get tanks, walk off the beach. And you are supposed to stay within your no-decompression limits. If something goes wrong, in theory you can surface immediately. The deco stop is a precaution only.
PADI does 40m IIRC, with its deep diving components. Other certification organizations are different.
Mauritius had fantastic diving, but the sites tend to start at 25m. I think I saw 60m sites listed among the well know locales, although the deepest my divemasters went the week I was there was 46m (deeper would need more complex decompression stops and multiple tanks for more than a minute or so at the bottom). I think NAUI was the predominant body on the island at the time.
I went down a rabbit hole on this yesterday, and PADI does 40, 45, and 50 meter certifications. Each has the previous one as a prerequisite, plus nitrox and others. Perhaps that's the reason I was told that PADI stands for "Put Another Dollar In".