Hot Pink vs Amethyst

How close are they?

ΔE 18.1, loose: different enough that you should pick on purpose. Amethyst is more saturated, cooler than Hot Pink.

Can I use Amethyst instead of Hot Pink?

Not as a straight swap; see the closer alternatives below. Loose match (ΔE 18). Amethyst is more saturated, cooler than Hot Pink.

Can I use Hot Pink instead of Amethyst?

The same difference applies the other way round: Hot Pink is 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.