ΔE 16.9, loose: different enough that you should pick on purpose. Amethyst Rayne is a little darker, more saturated, warmer than The Fang.
Not as a straight swap; see the closer alternatives below. Loose match (ΔE 17). Amethyst Rayne is a little darker, more saturated, warmer than The Fang.
The same difference applies the other way round: The Fang is a little lighter, more muted, 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 The Fang on the colour wheel See Amethyst Rayne on the colour wheel
All matches: The Fang equivalents · Amethyst Rayne equivalents