The sound not only depends on what kind of distortion but also on how much %%% there is in the sound. Like, how much milk and sugar in your coffee. An italian espresso with two spoons will be different from a sucky latte from a third grade vendor like Starbucks - not just in intensity and 'bean', but also in many other ways.
To name a few, mostly simplified:
2nd harmonic distortion: tubes, if done right, transistors, if done with low gain/low feedback
3rd harmonic distortion : transformers past their linear transfer curve
clipping : clipping...what? Clipping is when the signal exceeds the available voltage and transfer curve of the topology, it could be anything
AD converter cliping : see 'clipping'
mixing desk distortion : as many as there are different topologies of output line amps in the world : see 'clipping' Sansamp
: a fuzzbox with a mix knob
Compressor Distortion : which? VAC, FET, opto, vari Mu... or the transformers in the chain?
Overdriving the 1176
: input attentuator interaction with the gear feeding it, FET/depending on time constant, line amp, output transformer, ...
Overdriving the LA-2A : input transformer, tube stages, vactrol, interstage transformer, tubes, output transformer..