ΔE 24.9, loose: different enough that you should pick on purpose. Alien Purple is noticeably darker, much more saturated than Ignis Fatuus.
Not as a straight swap; see the closer alternatives below. Loose match (ΔE 25). Alien Purple is noticeably darker, much more saturated than Ignis Fatuus.
The same difference applies the other way round: Ignis Fatuus 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 Ignis Fatuus on the colour wheel See Alien Purple on the colour wheel
All matches: Ignis Fatuus equivalents · Alien Purple equivalents