ΔE 18.9, loose: different enough that you should pick on purpose. Imperial Purple is noticeably darker, much more saturated than Pastel Violet.
Not as a straight swap; see the closer alternatives below. Loose match (ΔE 19). Imperial Purple is noticeably darker, much more saturated than Pastel Violet.
The same difference applies the other way round: Pastel Violet 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 Pastel Violet on the colour wheel See Imperial Purple on the colour wheel
All matches: Pastel Violet equivalents · Imperial Purple equivalents