ΔE 18.5, loose: different enough that you should pick on purpose. Carmine Red is a little darker, more muted, cooler than Cherry Wood.
Not as a straight swap; see the closer alternatives below. Loose match (ΔE 19). Carmine Red is a little darker, more muted, cooler than Cherry Wood.
The same difference applies the other way round: Cherry Wood is a little lighter, 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 Cherry Wood on the colour wheel See Carmine Red on the colour wheel
All matches: Cherry Wood equivalents · Carmine Red equivalents