Volcanic ash is glass (the stone melts during an eruption due to the heat, then explodes into millions of splinters as clouds which lock down air travel because it melts again in the engines and destroys them) and can be found thousand of kilometers away afterean eruption (e.g. Yosemite eruption), creating a deadly environment for every animal where it's falling down.
Pyrolysis isn't exactly burning stuff, it's carbonizing it by heating without access to air. So no, it's not the same as wood ash because it's not ash.
Thank you for coming to my ~~Ted Talk~~ infodump.
It's very different from wood ash.