The 12AX7 is a high mu triode, with a high amplification factor and high plate resistance. It is suitable for situations needing lots of gain, and high(ish) output impedance. Examples would be microphone amplifiers, tone control amplifiers, phono amplifiers, and the input stage of power amplifiers.
The 12AU7 is a low mu triode, with a low amplification factor, and lower output impedance - it's useful for situations which involve driving a capacitive load like a long patch cord, or driving the grids of large output tubes. It is also excellent as a voltage amplifier stage where a moderate amount of gain is needed, for example in a line level preamp.
The 7199 is a triode/pentode, which contains one half which is very similar to half of a 12AU7, and the other is a high gain pentode, capable of much more gain than the 12AX7. This tube is the reason why Dynaco could get away with using one driver tube and not sacrifice performance too badly in the ST-70.
The 6GH8 is a television tube, and was used by the boat load by RCA in colour TVs in the 1960s. It was used in the sync circuitry, colour demod, etc. It is similar enough to the 7199 it can be used as a functional substitute now that the 7199 is rare and costly.
There are hundreds of other tube types, all tailored to a specific application. While it would be possible to use the 12AX7 for everything, you'd end up sacrificing performance big time. Same logic as wearing a single pair of tennis shoes summer, winter, rain, fall, to your job interview and then taking stuff to the dump. Yes you could do it, but is it a good idea? Thing about guitar amps, is they have very different performance requirements than hi-fi amps, so using only the 12AX7 doesn't leave a lot on the table performance wise.
