Bright Red vs Crimson

How close are they?

ΔE 27.7, loose: different enough that you should pick on purpose. Crimson is noticeably darker, more muted, cooler than Bright Red.

Can I use Crimson instead of Bright Red?

Not as a straight swap; see the closer alternatives below. Loose match (ΔE 28). Crimson is noticeably darker, more muted, cooler than Bright Red.

Can I use Bright Red instead of Crimson?

The same difference applies the other way round: Bright Red is noticeably lighter, 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.