This is not totally new as many places have volunteer fire departments - this extends the concept.
What's new or what's worse, is a huge "human needs" bureaucracy which fails entirely to actually meet those human needs despite soaking up a lot of money.
It varies in scale. Here in Santa Rosa, first responders actually did a good job in dealing with the fire. But in the post-fire situation, the effective emergency that those who lost their homes have at best a small chance to rebuild their lives isn't being dealt with - but then again it's just a more extreme symptom of the housing crisis, which isn't being dealt with 'cause that housing crisis is also a solution to the "how to we maintain financial markets" question.
But there you have a private-public complex everywhere that's taking up a lot of resources without giving backing enough or sometimes anything.
Typically you have first responders, and a network of mutual aid for broad scope disasters. During a major disaster, state level emergency management, state police or other get involved.
The level of competence and resources varies between states when it comes time for escalation.