ΔE 15.8, loose: different enough that you should pick on purpose. Walnut is a little darker, much more muted than Bullwhack Brown.
Not as a straight swap; see the closer alternatives below. Loose match (ΔE 16). Walnut is a little darker, much more muted than Bullwhack Brown.
The same difference applies the other way round: Bullwhack Brown is a little lighter, much 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 Bullwhack Brown on the colour wheel See Walnut on the colour wheel
All matches: Bullwhack Brown equivalents · Walnut equivalents