ΔE 25.7, loose: different enough that you should pick on purpose. Mummy White is noticeably lighter, much more saturated than Grey Mist.
Not as a straight swap; see the closer alternatives below. Loose match (ΔE 26). Mummy White is noticeably lighter, much more saturated than Grey Mist.
The same difference applies the other way round: Grey Mist is noticeably darker, 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 Grey Mist on the colour wheel See Mummy White on the colour wheel
All matches: Grey Mist equivalents · Mummy White equivalents