ΔE 30.8, loose: different enough that you should pick on purpose. Crimson is more muted, cooler than Pale Carmine Red.
Not as a straight swap; see the closer alternatives below. Loose match (ΔE 31). Crimson is more muted, cooler than Pale Carmine Red.
The same difference applies the other way round: Pale Carmine Red is more saturated, 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 Pale Carmine Red on the colour wheel See Crimson on the colour wheel
All matches: Pale Carmine Red equivalents · Crimson equivalents