ΔE 35.5, loose: different enough that you should pick on purpose. Cardinal Purple is noticeably darker, more muted, cooler than Orange.
Not as a straight swap; see the closer alternatives below. Loose match (ΔE 35). Cardinal Purple is noticeably darker, more muted, cooler than Orange.
The same difference applies the other way round: Orange 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.
See Orange on the colour wheel See Cardinal Purple on the colour wheel
All matches: Orange equivalents · Cardinal Purple equivalents