A fairly hot topic at the moment what with the US administration trying to sort out their healthcare system and bitching about the one that has worked 'successfully' in the UK since WW II.
In the UK there is the National Health System which is paid for by the state (so everyone who pays taxes is paying for its provision) the system has a base tier of GP's (general practitioner doctors) and above that hospitals where there are A&E departments (accident and emergency) for those moments when calling into the GP first would seem silly (oops I've cut my hand with the carving knife and I think my thumb's going to fall off - needs A&E, the local doc ain't gonna fix that) and all the other medical departments (urology, oncology etc etc)
Germany has the same kind of division of labour - roughly.
However in the UK when the GP thinks there's something wrong with you that he can't fix he'll write to the local hospital and you go on a list to see a specialist and you wait and you wait, could be months - unless it's something life threatening - a suspected lump in the breast gets seen very quickly. The waiting lists also vary considerably depending upon whereabouts in the UK you live (they call it jokingly the 'postcode lottery, except it's often not a joke, it can be a matter of life or death) BUT, you will be seen and treated and you wont have to pay for it - unlike the system in the US which they're trying to change.
There is also the option of private healthcare in the UK, you pay every month and then when you need treatment you often go to the top of the queue and often get treated in a nice sparkly new hospital.
In Germany there are three options (although only two official ones)
1. you can pay a top up (choosing your level - when I end up in hospital 'I want a room to myself' will cost more than the 'share with 3 others' option)
2. you go completely private
3. you pay nothing and pray you're never ill.
We have here what they call 'hausdoktors' and 'kinderarzt' so the adults get the GP style of doc and the kids get their own child friendly doc. When ill your first stop is of course this level of doc (unless you know it's SERIOUS - broken bones for example, been there, done that - twice) you make your appointment and are usually seen that day (in the UK you're lucky if you're still ill by the time you get your appointment through to see your GP) you pay 10 euros to the receptionist (this seems to be a 6 monthly cover charge that allows you repeat visits for the next 6 months free...no, I don't get it either) then you see the doc, if he can't fix you, you can guarantee he knows a man (or woman) who can and he'll make the call and get you an appointment right away.
My husband Simon has suffered with kidney stones in the long distant past so when he woke today with back pain he recognised it for what it was, and took himself off to the hausdok, the hausdok agreed with Si's diagnosis and referred him to a colleague along the road who specialises in the area. The 2nd doc had the equipment for the necessary scans and blood tests - which they did there and then and spotted the offending kidney stones. One prescription for pain relief and a check up appointment booked for 2 days time and Si was done.
The German health system works like clockwork, yes we have to contribute towards it but when you see it in action - wow!