ΔE 15.1, loose: different enough that you should pick on purpose. Carnage Red is a little darker, more muted, warmer than Blood Thorn.
Not as a straight swap; see the closer alternatives below. Loose match (ΔE 15). Carnage Red is a little darker, more muted, warmer than Blood Thorn.
The same difference applies the other way round: Blood Thorn is a little lighter, 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 Blood Thorn on the colour wheel See Carnage Red on the colour wheel
All matches: Blood Thorn equivalents · Carnage Red equivalents