ΔE 24.4, loose: different enough that you should pick on purpose. Crimson is a little darker, much more muted, warmer than Fuchsia.
Not as a straight swap; see the closer alternatives below. Loose match (ΔE 24). Crimson is a little darker, much more muted, warmer than Fuchsia.
The same difference applies the other way round: Fuchsia is a little lighter, much more saturated, 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 Fuchsia on the colour wheel See Crimson on the colour wheel
All matches: Fuchsia equivalents · Crimson equivalents