Somebody was just telling me that oxyacetylene torches cut steel by burning it - not melting. That's why they won't cut stainless steel, they can't burn it (oxidize it).
Plasma, cutters, on the other hand, cut by melting.
Oxy/fuel cutting is more like rapid oxidation than burning. The reaction is not self sustaining without fucktons of oxygen (you can burn basically anything if there's enough oxygen present). The oxygen stream helps blow away partially oxidized steel. It only works with steel because of the specific combination of metals other than iron in steel. It won't work on cast iron or stainless (though you can certainly melt them).
Plasma cutting liquefies the metal with electrical current then blows away the molten metal with air.
Take an oxy/fuel torch to a piece of wood and you will quickly have a self sustaining reaction even once the extra oxygen supply (torch) is removed.
Plasma, cutters, on the other hand, cut by melting.