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