ΔE 36.5, loose: different enough that you should pick on purpose. Mahogany Ink is much more muted, cooler than Brown.
Not as a straight swap; see the closer alternatives below. Loose match (ΔE 36). Mahogany Ink is much more muted, cooler than Brown.
The same difference applies the other way round: Brown is much more saturated, warmer.
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 Brown on the colour wheel See Mahogany Ink on the colour wheel
All matches: Brown equivalents · Mahogany Ink equivalents