ΔE 16.1, loose: different enough that you should pick on purpose. Azure is a little darker, more saturated, cooler than Amethyst Purple.
Not as a straight swap; see the closer alternatives below. Loose match (ΔE 16). Azure is a little darker, more saturated, cooler than Amethyst Purple.
The same difference applies the other way round: Amethyst Purple is a little lighter, more muted, 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 Amethyst Purple on the colour wheel See Azure on the colour wheel
All matches: Amethyst Purple equivalents · Azure equivalents