Yep, leaching hardwood ash with rainwater she produced mostly potassium carbonates and washing soda sodium carbonates similar to potash of the potassium hydroxide (potash) KOH which are normally less soluble when compared to sodium hydroxide, potassium salt tends to absorb less water, and are better for the soil or gardens, the leach is also good to use for removing fur while making rawhide or tanning leather, potassium salts or hydroxides are also better for making some of the other recipes like black powder, preserving food like dusting sweet taters, potash had many uses then and now...
Comparing KOH and NaOH there really is not much difference the both are used in similar applications in the chemistry of our grandparents and of what we use ourselves today.
Sodium hydroxide NaOH is normally cheaper, it is lighter than KOH, lighter in atomic molecular weight/Mol. produces more heat than KOH as an exothermic reaction with water, sodium hydroxide is used in water treatment while potash or KOH potassium hydroxide would be used in alkaline batteries, potassium hydroxide made a different soap than you will make with sodium hydroxide, the oil is broken to smaller particles, biodiesel, and many other products are made from these metal alkali hydroxides which have been and still are used in almost every chemical lab in the world throughout history we have used hydroxides such as potash or sodium hydroxide as well as other bases (the opposites of the acids) which are very useful reagents in grandmothers lab, as well as our labs today.
Either will dissolve or attack aluminum or tin...
Tin (Sn) will react with Potash or potassium hydroxide (KOH) and water (H2O), in an exothermic reaction releasing heat and hydrogen gases dissolving the tin as potassium-hexahydro stannate ...
Excess of a base or hydroxide will dissolve tin into solution.
Sn + 2KOH + 2H2O → K2[Sn(OH)4] + H2
more on tin reactions
https://chem.libretexts.org/Bookshelves/Analytical_Chemistry/Supplemental_Modules_(Analytical_Chemistry)/Qualitative_Analysis/Characteristic_Reactions_of_Select_Metal_Ions/Characteristic_Reactions_of_Tin_Ions_(Sn%C2%B2%E2%81%BA%2C_Sn%E2%81%B4%E2%81%BA)