For me, it's most likely the one strip of material hanging from a belt on both sides. (Two flaps hanging from a belt, hiding nothing, is the "half" style.) Or the loincloth becomes its own belt.
We really need a better taxonomy.
I tried out something at http://members.chello.at/diogenes/small_loincloth_dictionary.pdf
Corrections and suggestions welcome!
From what I remember reading, Weissmuller's loincloth was leather flaps with a chamois type material forming the U shaped under piece. The chamois naturally would provide a more comfortable fit and hold up to the constant water exposure.
For years I thought Weissmuller had worn some type of thong under his loincloth to "corral" him - especially in those scenes carrying Jane 😉 - but there is a scene in Tarzan's Desert Mystery where he was hiding in a cave during a sandstorm with Nancy Kelly where something is clearly peeking out. I'm surprised the censors didn't catch it.
I was watching Pony Soldier and I notice that one native american looks like he is wearing a jock strap under his flaps. Did indians wore jock straps back in the old west.