ΔE 9.7, close: similar, with a visible difference side by side. Orange Rust is a little lighter, warmer than Carmine.
Usually, if you are not matching paint already on the model. Close match (ΔE 10). Orange Rust is a little lighter, warmer than Carmine.
The same difference applies the other way round: Carmine is a little darker, cooler.
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 Carmine on the colour wheel See Orange Rust on the colour wheel
All matches: Carmine equivalents · Orange Rust equivalents