I've heard the Hitler called his national socialism "The Third Way." But I've seen no historical proof of that. I imagine it was some phrase thrown out by a third-rate Marxist scribbler and later adopted by left wing politicians. Marxists are good at making up stupid phrases that mean whatever they want it to mean.
Try reading a "soft law" document like the UN's Biodiversity Treaty. It's filled with verbs, adjectives and phrases honking nonsense at each other. Precautionary principle is one of their stupid phrases. It means that something must be done before something happens even if we don't have proof that it will happen. Kyoto and the global warming nonsense is one example of the precationary principle in action.
I think it might have been Nasser and DeGaulle (Ghandi was in that clique as well) that saw their militaristic, anti-US, independent from the USSR, Socializm to be the third way. I'm pretty sure Clinton's is derivative, he is not known for originality.