Dark Magenta vs Crimson

How close are they?

ΔE 19.2, loose: different enough that you should pick on purpose. Crimson is a little darker, more saturated, cooler than Dark Magenta.

Can I use Crimson instead of Dark Magenta?

Not as a straight swap; see the closer alternatives below. Loose match (ΔE 19). Crimson is a little darker, more saturated, cooler than Dark Magenta.

Can I use Dark Magenta instead of Crimson?

The same difference applies the other way round: Dark Magenta is a little lighter, more muted, 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.