Ash and bio char are two different commodity's and give different benefits. Through research it has been proven that the addition of bio char into agricultural compost provides many benefits to the end user.
1: greater water retention in the soil.
2: less compaction of the soil , enhancing root distribution.
3: locked in retention of microbial nutrients for vegetation to feed off.
4: a natural captured storage area for toxins, heavy metals, and NPK storage for for vegetation to acquire as needed.
5: the elimination of toxins, heavy metals and excess NPK leaching into ground water that contaminates our creeks , rivers, lakes and ground water.
6: An increase of yield in crop production of anywhere from 20% up to as high as 350% has been recorded by users in Europe, Australia, New Zealand and here in North America.
Bio char remains in the soil, continually working in it in a microbial way to enrich the soil for thousands of yrs. I just watched a documentary on this the other evening where it was used in the Amazon hundreds of yrs. ago to enrich the soil where other wise nothing would grow it's so acidic. Lots more info out there for those interested.