Ashen Stone vs Mummy White

How close are they?

ΔE 31.0, loose: different enough that you should pick on purpose. Mummy White is noticeably darker, much more saturated than Ashen Stone.

Can I use Mummy White instead of Ashen Stone?

Not as a straight swap; see the closer alternatives below. Loose match (ΔE 31). Mummy White is noticeably darker, much more saturated than Ashen Stone.

Can I use Ashen Stone instead of Mummy White?

The same difference applies the other way round: Ashen Stone 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.