ΔE 19.5, loose: different enough that you should pick on purpose. Gory Red is noticeably darker, much more saturated than Rust Orange.
Not as a straight swap; see the closer alternatives below. Loose match (ΔE 19). Gory Red is noticeably darker, much more saturated than Rust Orange.
The same difference applies the other way round: Rust Orange is noticeably lighter, much more muted.
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 Rust Orange on the colour wheel See Gory Red on the colour wheel
All matches: Rust Orange equivalents · Gory Red equivalents