ΔE 21.9, loose: different enough that you should pick on purpose. Mahogany Ink is more muted, warmer than Payne's Gray.
Not as a straight swap; see the closer alternatives below. Loose match (ΔE 22). Mahogany Ink is more muted, warmer than Payne's Gray.
The same difference applies the other way round: Payne's Gray is 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 Payne's Gray on the colour wheel See Mahogany Ink on the colour wheel
All matches: Payne's Gray equivalents · Mahogany Ink equivalents