You're talking about two different things altogether..... how the preamp works with the amp, and how the amp works with the speaker.
(And, in the context of tube and solid state gear, they are quite different.
The output of the amplifier sees the speaker as its load (and this is totally independent of what's connected to the amplifier's input).
Solid state amplifiers are generally designed to work with any normal speaker load with no special considerations.
Most good solid state amps will work with any speaker between 4 Ohms and 8 Ohms, and most will deliver more power into the 4 Ohm load.
(Most solid state amps deliver the same voltage into various loads; therefore a lower impedance load draws more power.)
Tube amplifiers are a little fussier about their load.
Tubes themselves are designed to operate into a very different load from your speaker (a typical tube expects a load impedance of several
THOUSAND Ohms).
Therefore, most tube amplifiers use a transformer to match the impedance of the tubes to the impedance of your speakers.
Transformers can be somewhat fussy; if they aren't matched correctly, you can end up with odd frequency response issues, or even distortion.
Therefore, most transformers actually include multiple outputs, each for a different speaker impedance (a 4 Ohm Output and an 8 Ohm Output).
(Some transformers make do with a single output tap. If your output has multiple taps, attaching a 4 Ohm speaker to an 8 Ohm tap may result in weak bass;
attaching an 8 Ohm speaker to a 4 Ohm output tap will sound good, but may deliver somewhat less power. )
As far as the preamp is concerned, the load the output of the preamp sees is the input of the amplifier (remember that this has nothing to do with the speaker).
Most tube amplifiers have a
VERY high input impedance.... often between 100k Ohms and 1 megOhm... and most tube preamps are designed with this in mind.
This means that many tube preamps have an output that is
ONLY suitable for driving a very high impedance load.
This is true for the majority of vintage tube preamps, and for many modern ones based on vintage circuit designs.
(Note that this isn't a problem as such.... but it can lead to compatibility issues.)
Most solid state amplifiers have an input impedance between about 10 kOhms and 47 kOhms.
This may be far lower than the load a particular tube preamp is designed to drive.
If this is the case, it can result in a very low output level, or even a noisy or distorted audio signal.
(Note that virtually all solid state preamps can easily drive a load of 10 kOhms or lower.)
Also, because of their high output impedance, many tube preamps have trouble with long interconnects, or interconnects with high capacitance.
If the capacitance of the interconnect is too high, it may interact with the output of the preamp to roll off high frequencies, resulting in muffled sound.
And, if the interconnect has poor shielding, it may be susceptible to picking up hum and other noise more easily than normal.
Unfortunately, better shielding, which improves the resistance to hum, also tends to make for higher capacitance.
As a result of this, short well-shielded interconnects are usually a good idea with tube preamps.
Note that many high quality tube preamps are in fact designed to be able to drive very low impedance loads - and work great with solid state amplifiers and long cables.
However, because this sort of problem almost never occurs with solid state preamps, it often doesn't occur to people to check the recommended load impedance for their tube preamp.
Now, another subject altogether is
PASSIVE preamps..... which is a fancy way of saying "a selector switch and a volume control potentiometer".
(There are other types of passive preamps... made with transformers or autoformers... but they are very expensive and we're ignoring them for now.)
A potentiometer-based passive preamp has no gain - it can turn down the level but not boost it.
This means that it won't work for you unless your source has more than enough output level to drive your amplifier.
These passive preamps also have a somewhat low input impedance, and a somewhat high output impedance.
This means that, like some tube preamps, they tend to interact with inputs that have a low impedance, and with cables that have a lot of capacitance.
They also tend to load their source somewhat heavily, and that load may vary considerably, potentially leading to a device that actually sounds different at different volume settings.
(The "payback" is that they cost very little, and produce no noise or distortion of their own, which makes them ideal in the narrow range of uses for which they are well suited.)
In general, a "passive preamp" would usually be a good choice to go between a solid state source device and a tube amplifier....
Will work acceptably between a solid state source device with a high output and a solid state amplifier with a relatively sensitive input....
And would usually be a bad choice to go between a tube preamp and a solid state power amplifier.
But exceptions do exist
(Note that, for devices like Schiit's combination "passive preamp and tube buffer", the options become somewhat more complicated.)
Is there someone here that can talk about the output impedance of the preamp and input impedance of the amp and speaker load ?
If I remember right, not all preamps and amps go together but tube gear mixed with solid state is even more dependent on impedance. I always ran solid state preamps into tube amps. I was just reading that Schiit Audio's two new Tube Passive/Active preamps the Saga and Freya when mated to there new Solid State Vidar Stereo/Mono Power Amplifier can not be configured certain ways.
