ΔE 19.2, loose: different enough that you should pick on purpose. Brown Wash is noticeably darker, more muted than Warm Skin Shade.
Not as a straight swap; see the closer alternatives below. Loose match (ΔE 19). Brown Wash is noticeably darker, more muted than Warm Skin Shade.
The same difference applies the other way round: Warm Skin Shade is noticeably lighter, more saturated.
ΔE is the colour difference between our two swatch estimates: under about 6 is close, over about 15 is loose. Real paints also differ in finish, coverage and how they thin, so test before you commit.
See Warm Skin Shade on the colour wheel See Brown Wash on the colour wheel
All matches: Warm Skin Shade equivalents · Brown Wash equivalents