ΔE 18.1, loose: different enough that you should pick on purpose. Alizarin Crimson Hue is a little darker, much more muted than Blood Thorn.
Not as a straight swap; see the closer alternatives below. Loose match (ΔE 18). Alizarin Crimson Hue is a little darker, much more muted than Blood Thorn.
The same difference applies the other way round: Blood Thorn is a little lighter, much more saturated.
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 Alizarin Crimson Hue on the colour wheel
All matches: Blood Thorn equivalents · Alizarin Crimson Hue equivalents