You have a great many things mixed up - first thing is that DMR is of course digital, while SSB, is usually HF - although it is also used on 2m and 70cm for long distance comms - but ham radio, is very different - it’s a hobby with multiple facets - some just chat locally, others chat from america to the UK on a handheld radio, using the internet for the long haul, only existing as real radio at the two ends. You can talk about radio hams, but you cannot say HAM as if it is a ‘thing’ - it is simply short for amateur. So gatekeepers of ham radio makes sense.
The best way to explain how amateur radio works is to use the analogy of a club. You could be a club of one, but it’s pointless. Ham radio requires you to pass an exam. You can pick levels of difficulty and your licence reflects your status and what you can do. Lots of people just cannot get used to the fact that if you don’t fit in, your success is always limited. Etiquette is a must. Abrasive folk simply call their heads off and get no answers and get angry. Nice people always get responses - people forget this.
I suppose radio types boil down to this, no matter where you are in the world, most regions have very similar systems.
Business licences - set aside frequencies for businesses to communicate with themselves. Company A does not talk to company B, and users just get given radios - usually small or medium areas. In the UK, price can be cheap. A system covering a small town might cost just £75 for 5 years. If you want to talk to a whole county, it is much more expensive, and the whole country is a huge outlay for the licence. Here, we can share a few channels with others, and accept occasional annoyance. Radios tend to be programmed to NOT receive anything other than your own people, but not hearing them doesn’t mean they are not there - and sometimes interfere with each other. In the UK, OFCOM oure version of your FCC also offer what they call technically assigned frequencies. Mine gives me a transmit and receive frequency that is not in use by anyone locally. It costs £75 annually, so more expensive than the simple licence.
Small businesses and individuals can also use what we call PMR446 - a licence free system - 16 channels, low power and totally uncoordinated - your skip delivery company might get hordes of kids messing around so uncontrolled and occasionally unusuable. To make it worse, some hobby people use it to talk to each other - often with far more power and better antennas. Our Government just let them get on with it. In the US, you have similar systems FRS and GMRS. Similar but different. Your FCC introduced controls on the type of radios that are legal. Again, in the US, people use the systems in a way that the FCC is not keen on. From what I hear, they just don’t have the manpower or budget to police it, but again, like in the UK - it is illegal, like speeding in your car.
Ham radio is a world wide concept - common(ish) frequencies with the entire purpose being experimentation and self-training. You are expected to understand the science, and police yourself. Hence why people misbehaving often get reported to the authorities. Some hams are highly skilled, very clever folk and others are thick, only just scraping through the simplest level of testing. Others have PhD’s in rocket science. Until digital came along, VHF and UHF was mainly FM based. SSB and good old Morse Code on the HF long distance bands. Some hams specialise in building antennas, and some even fire off Morse Code at the moon and people on the other side of the world catch it’s reflection. Some use satellites, others are into microwave comms and data.
Lastly - you mention DMR and public repeaters. I cannot comment on the US, but here business DMR would be on a businesses own repeater, or a shared community one, usually with payment. You mention how it is coordinated. Here, even in smaller cities, it can be very hectic, and OFCOM cannot guarantee a channel can be unique to one user. Many users, though are dumping radio systems in favour of the cell system - IP based radios that use a cellular data card, but work like old fashioned radios. Most countries do NOT allow encryption, but there is a lot of encrypted digital radio here. It is just one tick box in the programming, after all. Hams don’t encrypt as a thing, because they want to be heard by others. encyption ruins the ham ethos. They call CQ endlessly, looking for a response. encryption rather ruins that. Part of the learning you have to do explains about the science - we had 25KHz channel spacing, then went to 12.5KHz. This dictates the space one channel uses up, so also explains why you can’t transmit ON the band edges, but must be a little within it. 25 vs 12.5 gives a bit of extra space. Remember too that 1MHz is half of the entire UK band - 144-146 is what we have, with a few licence holders having a bit more. CB is exacty what it says - a band for citizens. Your Government set aside some channels, gave them 4W to play with. FRS and GMRS are sort of similar, BUT, my understanding is they were not intended to replacement for CB - which is for anyone to talk to anyone. The Family radio service has a clue in the title, and GMRS is sort of well, general for a wider range of uses. You can find all this info on the FCC site and you have the ARRL for ham information. We have the RSGB in the UK. Not all hams agree with the aims and rules of these organisations, but the authorities do - often letting them sort out problems. Things like interference, or planning for antennas, and they also produce a framework - using band plans. unofficial ‘suggestions’ for where certain things happen, frequency wise. The law does not say radios hams have to stick to these, but most people do. if you want to just chat, there is no point using a channel that other people are doing digital data on.
What it boils down to is a few questions. Who do you want to talk to? Do you need local or worldwide coverage? Is it just a hobby, or do you have business use in mind? Have you a specific need? Many US folk have this thing about being prepared. We do not have this in the UK. US folk build bunkers, prepare for the day power is cut and they are on their own. Their needs are different from a guy who wants to sit in a little shed, trying to hear somebody in a far away country sending more code on a radio with power output from a solar cell supply. Now we have digital radios capable of storing the callsign and name of everyone in the whole world, so when they hear somebody, it says Paul G4RMT Lowestoft, England. The fact they might be in another country is now immaterial, the internet is doing the hard work. Very different ham radio.
To finish, you also have to accept one other thing. If a ham hears an idiot, or somebody clearly unpleasant, all they do is not respond. Newcomers often mark their own card. They call. dozens of people hear them but do not reply. I have been a ham for 45 years. In the past year I have talked to 2. I am now old, and a dinosaur. I just don’t have enough hours to live to waste them on the people I hear. The locals are not horrible or nasty, in fact I have met many of them, but what would we talk about?