ΔE 33.7, loose: different enough that you should pick on purpose. Orange Rust is noticeably lighter, warmer than Pure Red.
Not as a straight swap; see the closer alternatives below. Loose match (ΔE 34). Orange Rust is noticeably lighter, warmer than Pure Red.
The same difference applies the other way round: Pure Red is noticeably 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 Pure Red on the colour wheel See Orange Rust on the colour wheel
All matches: Pure Red equivalents · Orange Rust equivalents