Dark Sky vs Amethyst Rayne

How close are they?

ΔE 15.8, loose: different enough that you should pick on purpose. Amethyst Rayne is noticeably lighter, warmer than Dark Sky.

Can I use Amethyst Rayne instead of Dark Sky?

Not as a straight swap; see the closer alternatives below. Loose match (ΔE 16). Amethyst Rayne is noticeably lighter, warmer than Dark Sky.

Can I use Dark Sky instead of Amethyst Rayne?

The same difference applies the other way round: Dark Sky is noticeably darker, 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.