Rust Orange vs Carmine Red

How close are they?

ΔE 17.7, loose: different enough that you should pick on purpose. Carmine Red is noticeably darker, more saturated, cooler than Rust Orange.

Can I use Carmine Red instead of Rust Orange?

Not as a straight swap; see the closer alternatives below. Loose match (ΔE 18). Carmine Red is noticeably darker, more saturated, cooler than Rust Orange.

Can I use Rust Orange instead of Carmine Red?

The same difference applies the other way round: Rust Orange is noticeably 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.