They are similar, in that they both involve soaking milled malt and grains in hot water.
There is less going on with steeping. You use the steeping technique when you are brewing an extract beer and getting your fermentables from the extract. Then you steep selected grains to add flavor and color.
With mashing, you are not just extracting flavor and color, but also you are getting fermentable sugars from the grain. To do this, you are providing the conditions necessary for enzymes to be activated and convert some of the starches into sugars. This requires that a base malt such as two-row barley malt be a part of the mash and it also requires strict attention to temperature, because the enzymes are temperature specific.
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