From the beginning, distillation was used to separate liquids that had different boiling points.
In the making of potash, you are evaporating, not distilling. So product would be an evaporate.
evaporate
vt.
L evaporatus, pp. of evaporare < e3, out, from + vaporare, to emit vapor < vapor, VAPOR6
1 to change (a liquid or solid) into vapor; drive out or draw off in the form of vapor
2 to remove moisture from (milk, vegetables, fruits, etc.) by heating or drying so as to get a concentrated product
3 a) to deposit (a metal, metallic salts, etc.) by evaporation b) to drive out (neutrons, electrons, etc.)
vi.
1 to become vapor; pass off in the form of vapor
2 to give off vapor
3 to disappear like vapor; vanish
e[vap#o[ra4tion
n.
e[vap$o[ra#tive
adj.
e[vap$o[ra#tor
n.