Fuchsia vs Amethyst

How close are they?

ΔE 32.7, loose: different enough that you should pick on purpose. Amethyst is noticeably lighter, more saturated, cooler than Fuchsia.

Can I use Amethyst instead of Fuchsia?

Not as a straight swap; see the closer alternatives below. Loose match (ΔE 33). Amethyst is noticeably lighter, more saturated, cooler than Fuchsia.

Can I use Fuchsia instead of Amethyst?

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