ΔE 23.2, loose: different enough that you should pick on purpose. Ink Magenta is more muted, cooler than Alizarin Crimson Hue.
Not as a straight swap; see the closer alternatives below. Loose match (ΔE 23). Ink Magenta is more muted, cooler than Alizarin Crimson Hue.
The same difference applies the other way round: Alizarin Crimson Hue is 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 Alizarin Crimson Hue on the colour wheel See Ink Magenta on the colour wheel
All matches: Alizarin Crimson Hue equivalents · Ink Magenta equivalents