I hadn't read your initial post before.... and there is one misunderstanding that needs to be corrected.
It is the ENERGY, and not the voltage or current specifically, that determines how much power an amplifier can deliver.
In a typical modern audio amplifier...
Tube amplifiers operate at high voltage and low current (relatively)...
While solid state amplifiers operate at higher current and lower voltage...
The reason why tube amplifiers need an output transformer is that the voltage and current they operate at aren't a very good match for modern low impedance speakers.
(In the way old days there were very high impedance speakers that could be driven directly by tubes... but they haven't been made in a very long time.)
(It is actually quite possible to drive an electrostatic speaker directly with a tube, and this is often done with headphones, but rarely seen for larger speakers, which typically require even higher voltages...)
In terms of the "basic operation of a typical amplifier"...
You have a power supply - and one or more active devices that "sit between the power supply and the speaker and control the flow of current to the speaker in time to the music".
This process happens EXACTLY the same way for a typical Class A or Class A/B tube amplifier and for a typical Class A or Class A/B solid state amplifier.
One side of each output device is connected to a supply rail and the other side is connected to the output.
In a solid state amplifier the output stage is normally connected directly to the speaker (in some older designs a coupling capacitor was used).
In a tube amplifier the output stage is connected to the speaker through a transformer (which matches the impedance of the output tubes to the impedance of the speaker).
(The output transformer couples the AC portion of the audio signal to the speaker while allowing the DC plate current to pass through it largely unaffected.)
However, in both cases, the output devices exercise a form of variable control over "the current that flows to the speaker in time to the music".
Note that this process may be very different for other types and classes of operation...
For example, in a Class H amplifier, the power supply voltage feeding the output devices may switch between two or more different levels.
(Class-H is often used in solid state designs to improve efficiency but I've never seen a Class-H tube amplifier.)
Other than that Class-H is identical to ordinary Class-1 or Class A/B.
In a Class-D amplifier, the power supply is connected to a switch, which switches on and off very fast, and delivers current as a series of variable width or variable frequency pulses...
And, just as with a DAC, this switched high frequency signal is then passed through a "reconstruction filter", which converts it into a normal analog signal.
It is quite possible to build a Class-D amplifier using tubes...
However the complexity outweighs the benefits, and tubes don't work quite as well in this application as switches, so very few Class-D tube amps have ever made it to market...
Tubes, especially the sort used for audio applications, are inherently high voltage high impedance devices.
As such they operate from a power supply that supplies higher voltage and lower current...
And, as such, they require filter capacitors that operate at much higher voltages...
But, since much lower current is involved, those capacitors can have much lower capacitance value...
(And, yes, overall energy varies as the capacitance value, and as the square of the voltage.)
If you want to be technically correct, in almost all common tube circuits, you will see that the power supply voltage is NOT applied directly to the tube at all.
In most tube preamp circuits there is a plate resistor between the power supply and the tube.
The tube actively controls the current through itself... and the output signal is actually taken from the voltage drop across the plate resistor.
And, in the output stage of a typical tube power amp, the output transformer sits between the output tubes and the power supply.
The output transformer "couples" the AC (audio) portion of the output current to the speaker...
While allowing the DC portion of the plate current to pass through it relatively unaffected...
And, yes, tube amplifiers tend to operate from very dangerous voltages that can easily kill you if you aren't careful...
However, to be fair, even 50V can be dangerous under some conditions, so care is ALWAYS advised.
I've gotten really interested lately in tubes and tube amps.
Besides the obvious differences, especially in a dark room, what else can be said?
Some talk about he difference in distortion products. Even VS Odd harmonics. That sort of thing.
But I looked at the Power Supplies. THIS is a real eye opener. Tubes ALWAYS have full PS voltage applied to them.
Not like SS which turns the voltage on / off basically in time to the music.
One thing which caught my eye were the smaller capacitors in tube amps. Certainly nothing like the number or capacity of SS gear.
When I checked into that? Here's what I found. While capacitance is important, the VOLTAGE is what really drives what matters.
It 'is NOT capacitance, but ENERGY. Usually expressed in Joules. A 100mfd cap @500volts has about the same energy as 4000mfd @80volts for a SS amp.
Energy stored rises VERY quickly with voltage. .
This is where Voltage or Current source amps and the difference start. Tubes seem to always have the full voltage applied while SS is biased to an slight 'on' state and floats from there....
Just be CAREFUL when messing around under the hood of a tube amp. 500v will REALLY smart if you zap yourself.
Somebody with more informatin might want to add to this, but for now? I'm satisfied with just the first layer.