My understanding is that "steeping" is used for grains that do not need any type of enzyme conversion, usually the specialty grains like Caramel/Crystal, Chocolate, etc. This is because these grains have been roasted to a high temp and all of the available sugar is crystallized, there is no remaining starch to convert. So steeping dissolves the sugar that is crystallized in the grain.
"Partial mash" is done when you DO need to perform enzyme conversion on the grain. It's partial because you generally are mashing a small portion of the grain bill and using extract for the remainder.