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In the early days they didn't have modern first stage set-ups
You had a round "first stage" about the size of a small dinner plate and two hoses going into/out of it.
This was essentially a semi-closed circuit regulator.
Air would be breathed and then sent back to the first stage which would eventually release excess air. I don't remember if there was any major scrubbing going on.
Eventually the first single hose regulator (AKA open circuit) was made and this is where the distinction came from.
As for where the terminology came from, I don't know the exact history timeline for it.
Ermm... BZZZZZZZT.
Twin-Hose regulators (both single stage and twin stage) are open circuit as well. No air is recycled. And yes, just because it's a big box on the tank valve does not mean that it doesn't have 1st and 2nd stages. (Earlier designs regulated tank pressure to ambient in a single stage, later on, similar to two stage single hose regulators, a 1st stage regulated to intermediate pressure, and a 2nd stage regulated intermediate to ambient, although both were included in the same box).
Semi-closed is a variation of closed circuit, where instead of just adding O2 as it is depleted, part of the breathing loop is replaced with a fresh gas mix, either constant flow or breathing controlled.
AFAIK the open circuit / closed circuit terminology is as old as sports diving (Cousteau with open circuit, Hass with closed circuit)
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