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I don't know if these two articles explain it, but the difference is that full mould casting uses a bonded sand, usually with a coating of a refractory investment first, lost foam uses an unbonded sand.
I expect that you can find sources, of varying credibility, to define either term in any way you like. Certainly lost foam is sometimes used as a blanket term for both. Andy Dingley (talk) 20:21, 10 April 2014 (UTC)