ΔE 20.7, loose: different enough that you should pick on purpose. Royal Purple is noticeably darker, much more saturated, warmer than Periwinkle Purple.
Not as a straight swap; see the closer alternatives below. Loose match (ΔE 21). Royal Purple is noticeably darker, much more saturated, warmer than Periwinkle Purple.
The same difference applies the other way round: Periwinkle Purple is noticeably lighter, much more muted, 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 Periwinkle Purple on the colour wheel See Royal Purple on the colour wheel
All matches: Periwinkle Purple equivalents · Royal Purple equivalents