ΔE 27.9, loose: different enough that you should pick on purpose. Mahogany Ink is noticeably darker, more muted, warmer than Purple INK.
Not as a straight swap; see the closer alternatives below. Loose match (ΔE 28). Mahogany Ink is noticeably darker, more muted, warmer than Purple INK.
The same difference applies the other way round: Purple INK is noticeably lighter, more saturated, cooler.
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 Purple INK on the colour wheel See Mahogany Ink on the colour wheel
All matches: Purple INK equivalents · Mahogany Ink equivalents