Interesting! I'm familiar with the Greek process but not Spanish or Californian, thought they were all pretty much the same, except for harvest time.

There's a fourth way olives are consumed (and probably the most common: olive oil. Explanation of how the oil is produced here:

https://www.oliveoil.com/how-is-olive-oil-made/

I'd also point out that wood ash is what lye was originally made from. Decent how-to here: https://www.diynatural.com/how-to-make-lye/