I am struggling to find references at the moment, but from what I remember, due to the history of putsches etc, in Germany the army could for a long time not be deployed internally. So while in other countries the actual army pioneers would be called in to clear roads after a flood, this was not possible in Germany. So the solution was to build a civil version of this, which as a side-effect was actually completely independent of the armed forces. Since the army cannot use these capabilities offensively, this structure helps calming twitchy neighbours after starting two world wars in a row. It is one of many examples of decentralisation of powers and capabilities in post WWII Germany.
The lines between different volunteer forces and structures are probably converging globally and most countries have similar capabilities available within their volunteers. Looking up the SES, it seems to be doing a lot of things including heavy lifting and rescuing people from cars crashes. The very specialised THW would only do the first, and (volunteer?) fire services do the second. If that is worth the distinction (and this post), I dont know. But it probably leads to the THW volunteers having much pride in being called in when the equipment of the fire service is not good enough, while seeing very little action and have therefore a lot of time to support the local brewer.
We also have the Cajun Navy in the Southeast who will help around the Gulf states after Hurricanes. They are mainly small boat owners who will aid in rescuing people stuck in their houses.
There are volunteer crews here in Canada, but they are almost exclusively for smaller towns less than 10k. Not much distance to travel to their station, however a house on my street burned pretty much to the ground waiting for the volunteer crew to arrive.
The trick to compensate for that is volume. As many stations as possible with only a few vehicles (mostly a single very large truck with 2000 litres of water), so ways are short. Only when something bigger happens, multiple stations will be alerted. Some stations also specialize by having a ladder truck, a hazmat truck, etc.
Volunteers should not be 10 minutes or more away from the station when on call. They can also cross on red in their private vehicle when alerted.
The main benefit the fire brigade offers is the ability to prevent spread to other buildings, and assist people escaping.
1) Anyone trapped may end up dying or being severely injured 2) Fire spreads to neighbours (in the case I described the owners and neighbours were hosing down the next door house at their own risk.
Where I lived in Germany (city of ~300k) the next paid fire brigade was a ways off from our suburb. However, as it was explained to me, house building permits aren't issued if the next paid fire station is too far away (dunno what the time limit is) and volunteer forces don't count into that radius. However we had a volunteer fire brigade right smack middle of town (this isn't the sort of planned American suburb, this was a regular town founded around the year 1100 and the larger city grew into/around it). 3 fire trucks for ~6k inhabitants. 2 minute drive to us. Closest regular fire brigade would have been about a 7 minute drive but part of a rural town 'next door', closest actual city fire station ~15 minutes.
Where I live now in Canada (town of ~20k and growing) it's mainly a volunteer force. We have 6 fire engines + paramedic. There are IIRC a couple of paid firefighters always in the station just in case and the rest are volunteers that are at max allowed to live/work about a 10 minute (IIRC) drive from the station. Been a while since the open house visit. Next town over with a paid fire brigade is about a 12 minute drive from here while the local fire station is a 2 minute drive (without sirens blazing :)) I think they have a good chance of being faster or on par.
On the other hand, that 300k town had its own paramedic services helicopter. Had to unfortunately "make use" of that once. Awesome experience (apart from the medical emergency part). But if you have a medical emergency going on and you start hearing that chopper way before you hear sirens, it's just awesome!
Where I live now (in a millions of people metro area, there is no medical helicopter service whatsoever and traffic is really really bad.
And in non-disaster times those voluntary organisations do like to put on gatherings and have a beer or 10... I guess you can add that to the list, too.
I suppose the SES (State Emergency Service) is the equivalent of the THW, even to the point of being set up at about the same time to help in case of a war but dealing with natural disasters and other incidents that are less dramatic. THW is federal but SES is state, but I'm sure that's trivial.
Police are of course paid.
Paramedics who ride in ambulances attending emergecies are paid - perhaps not enough. But first aid at festivals and larger events are handled by organisations like St Johns Ambulance, which are mostly volunteer-based organisations. It sounds like perhaps it is structurally different, but has the same effect.
Firefighters are divided. Metropolitan firies are usually paid, but in country towns they are volunteer.
I have noticed many similarities between Australia and Germany that seem surprising. Perhaps this is another one to add to that. Maybe it isn't so surprising though. It would seem like every country town couldn't have its own firefighting force if they have only very rare fires or if they are particularly seasonal.