I suppose there are various names in use for such. You took that pic from
Solid Brass dog clip products, buy Solid Brass dog clip products from alibaba.com where it's called a Dog clip, and they are useful for such. I'm not sure where I picked up the name bolt clip - hardware store, divers, my mind...?
I think my LDS tried to sell me a spring tether kinda like your description but I declined. I have enough hanging around with my slung pony and two second stages. I like my camera strapped to my wrist. I was concerned about losing it while swimming with whale sharks, no strobe or float strap, negative in the murky water, etc. but kept it tight on my wrist ok. Now I have one slightly positive and the float strap as well.