ΔE 19.7, loose: different enough that you should pick on purpose. Carmine Red is a little darker, much more muted, cooler than Firethorn Brown.
Not as a straight swap; see the closer alternatives below. Loose match (ΔE 20). Carmine Red is a little darker, much more muted, cooler than Firethorn Brown.
The same difference applies the other way round: Firethorn Brown is a little 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 Firethorn Brown on the colour wheel See Carmine Red on the colour wheel
All matches: Firethorn Brown equivalents · Carmine Red equivalents