ΔE 19.5, loose: different enough that you should pick on purpose. Amaranth Red is noticeably lighter, more saturated, warmer than Fire Red.
Not as a straight swap; see the closer alternatives below. Loose match (ΔE 20). Amaranth Red is noticeably lighter, more saturated, warmer than Fire Red.
The same difference applies the other way round: Fire Red is noticeably darker, 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 Fire Red on the colour wheel See Amaranth Red on the colour wheel
All matches: Fire Red equivalents · Amaranth Red equivalents