Uneducated imho: "wootz" is when you have distinctive iron carbide and austenite, while sham is when you have ferrite/pearlite structure.
"Differential" tempering willl produce a small region with martensite on top of a simple ferrite. In addition to this, the properties will depend on various impurities - vanadium, molibden, sulfites etc., and on geometry - uniformity and thickness of layers.
In short all of these are not techniques to enrich carbon context, but more of a final result of different processes. The properties of wootz, mechanical damascus and differentially tempered weapons are also going to be drastically different, whith no sure way to say which one is better until very late XIX century when I think european steel simply became vastly superior to anything else - experiments with Moser collection, experiments done by russian and english cavalry weapons at least seemed to show this.
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