ΔE 22.6, loose: different enough that you should pick on purpose. Crimson is a little lighter, cooler than Reddish Orange.
Not as a straight swap; see the closer alternatives below. Loose match (ΔE 23). Crimson is a little lighter, cooler than Reddish Orange.
The same difference applies the other way round: Reddish Orange is a little darker, 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.
See Reddish Orange on the colour wheel See Crimson on the colour wheel
All matches: Reddish Orange equivalents · Crimson equivalents