ΔE 46.2, loose: different enough that you should pick on purpose. Mahogany Ink is noticeably darker, much more muted, cooler than Transparent Ochre.
Not as a straight swap; see the closer alternatives below. Loose match (ΔE 46). Mahogany Ink is noticeably darker, much more muted, cooler than Transparent Ochre.
The same difference applies the other way round: Transparent Ochre is noticeably lighter, 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 Transparent Ochre on the colour wheel See Mahogany Ink on the colour wheel
All matches: Transparent Ochre equivalents · Mahogany Ink equivalents