ΔE 6.9, close: similar, with a visible difference side by side. Smoke Ink is more muted than Ashroot. They are different kinds of paint: Army Painter Ashroot is an opaque base/layer paint and Vallejo Smoke Ink is an ink, glaze or transparent paint, so they won’t behave the same on the model even where the colour is close.
Usually, if you are not matching paint already on the model. Close match (ΔE 7). Smoke Ink is more muted than Ashroot. They are different kinds of paint.
The same difference applies the other way round: Ashroot is more saturated.
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 Ashroot on the colour wheel See Smoke Ink on the colour wheel
All matches: Ashroot equivalents · Smoke Ink equivalents