One model, two finishes
Choose stonewash if you want a scuffed texture that, by Kershaw's account, helps hide scratches and fingerprints; choose satin if you prefer the look Kershaw describes for its own satin finish, typically a faint pattern of vertical lines across the blade. Both descriptions are about look and how visible wear is, and neither finish changes the steel underneath.
Stonewash or satin is a choice about looks and about how much wear you want to see. Kershaw's entries for these two finishes and Boker's stonewash entry are about how a blade looks and how easily scratches and fingerprints show on it; none of them mentions cutting.
If you would rather not notice marks from use, stonewash fits: Kershaw says it helps hide scratches and fingerprints. If you like the look of a satin blade, that is reason enough to pick it. Neither Kershaw nor Boker says satin wears worse; Boker's remark about marks standing out is about a polished blade.
The finish is the surface, not the alloy. The Civivi Elementum Linerlock in the grid below shows it: the Burgundy listing's spec table prints D2 tool steel with a stonewash finish, and the Gray listing prints D2 tool steel with a satin finish, each with a 3 inch blade, a linerlock and a G10 handle. The Boker Plus Kwaiken Air Mini pair beside it does the same in VG-10 stainless. The supplier descriptions call both stonewash blades in the grid black stonewash, so blade color differs as well as texture. Whether a dark stonewash blade also carries a coating is a question for the maker's product page; blade coatings are their own subject.
The answer on reading a knife spec sheet shows where the finish sits on a product page.
Some blades settle the question for you. Kershaw says it sometimes combines two finishes on one blade, for example satin on the blade flats and stonewash on the grinds. Kershaw defines the flat as the face of the knife without any grinds, and the grind as how the blank is thinned so the blade gets thin enough along the edge to cut.