Dark Wood vs Mahogany

How close are they?

ΔE 16.4, loose: different enough that you should pick on purpose. Mahogany is much more muted, cooler than Dark Wood.

Can I use Mahogany instead of Dark Wood?

Not as a straight swap; see the closer alternatives below. Loose match (ΔE 16). Mahogany is much more muted, cooler than Dark Wood.

Can I use Dark Wood instead of Mahogany?

The same difference applies the other way round: Dark Wood 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.