I can add one technical diver's input on this...

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The terminology was different in tech training, to reflect the different role a fellow diver plays on the dive. My fellow student was not referred to as my buddy, but instead was my "team mate".
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ALOT of things are different in tech though, and some of the challenge for divers with even decades of recreational diving experience (as my team mate during training has been a recreational dive instructor for probably almost as long as I've been breathing), is UN-learning some things to learn the new.
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And though we're taught independence, self-reliance, redundant-everything, and ALWAYS have a plan B, plan C, and a plan D that does not require another diver to execute...we were also taught team-work, and diving with another (appropriately trained and outfitted) diver can provide one major thing that can be supplied no other way ..... a "redundant brain". But, yes, a tech diver IS trained to "be your own buddy".
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I do some dives that I wouldn't dream of doing without my most trusted team mate.

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Yet, I also do many "independant dives" now, where there are other divers around in the water, but we generally are paying minimal attention to each other 'till we're all back on the boat, or hanging out on the deco line together.
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I ONLY do these dives, however, in Full Tech Gear, with a specific plan, and dive that plan.
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I did alot of my (non-wreck-penetrating) dives this way in Truk Lagoon. ...and often those dives ended with me being last in the water (hooray for a low SAC rate! <grin>) doing my last couple of deco stops alone (sometimes in the dark, as the others started dinner!)
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When I am in recreational gear, I only do recreational dives: No deco, appropriate limits, and with a buddy.