ΔE 57.7, loose: different enough that you should pick on purpose. Mahogany Ink is noticeably darker, much more saturated than Transparent White.
Not as a straight swap; see the closer alternatives below. Loose match (ΔE 58). Mahogany Ink is noticeably darker, much more saturated than Transparent White.
The same difference applies the other way round: Transparent White is noticeably lighter, much more muted.
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 White on the colour wheel See Mahogany Ink on the colour wheel
All matches: Transparent White equivalents · Mahogany Ink equivalents