Fire Orange vs Amaranth Red

How close are they?

ΔE 16.9, loose: different enough that you should pick on purpose. Amaranth Red is a little darker, cooler than Fire Orange.

Can I use Amaranth Red instead of Fire Orange?

Not as a straight swap; see the closer alternatives below. Loose match (ΔE 17). Amaranth Red is a little darker, cooler than Fire Orange.

Can I use Fire Orange instead of Amaranth Red?

The same difference applies the other way round: Fire Orange is a little lighter, 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.