I guess this is a big topic potentially. I'm just trying to understand first, in what ways do amps differ tonally and how much of that does does not ultimately come down to frequency response characteristics that can be adjusted with tone controls or an EQ pedal. Secondly, I'm curious which of these characteristics can modelling amps successfully approximate.

So I think I'm on safe ground by assuming that the frequency characteristics of different amps often ARE differernt and I would think that this COULD, at least in principle, be manipulated with tone controls or EQ pedals/software. That is, maybe amp A is more boomier than amp B but you could increase the bass knob and maybe decrease the treble knob on amp B to bring it into the same frequency realm as Amp A.

Do different cabinet/housing designs (e.g., closed vs open back) affect amps in ways other than simple frequency response. I have seen amps or software that let's you select different cabinets. But the amp itself has a particular housing (e.g., open vs closed back) so how successful can an open backed modelling amp be at replicating the sound of a closed back amp. If the difference is just that one is more bassier than the other, I would think that this could be modelled by adjusting the EQ. But maybe it is more, or other, than that.

Then there is, I would guess, the dynamics of the response of one amp compared to another. That is, as the gain or input to one amp increases, maybe it starts to compress and saturate sooner than another. I have no idea how modelling amps do what they do, but I would think that this is one of the main things that modelling amps try to simulate insofar as all of the modelling amps I've seen have settings for "American" vs "Brit" etc (even if they don't use that term [like ISF on Blackstar amps]) style and I think that's one of the main differences.

Speaker size. Well, if a given modelling amp has a single 8" speaker, I would think it is fundamentally incapable of accurately simulating a Fender Twin Reverb for example with it's 2 12" speakers. Like the saying about not being able to get blood from a turnip. But how much does speaker configuration contribute to the unique (I presume, haven't heard one in person) sound of a Fender Twin? Can a modelling amp, maybe with a smaller speaker, recreate something like this just at a lower volume?

Related to this, I hear people talking (or see them writing) about the unique and powerful sound of a stack, for example- one that "moves a lot of air." Is moving a lot of air something that you only get with big speakers driven by a high watt amp? Does it basically equate to volume? Will a high wattage amp with a big speaker(s) move a lot of air even at a low volume? Or does a big high-wattage amp at low volume sound like a small wattage small speaker amp at a higher volume. Are smaller speakers (like the twin 3" speakers on a Yamaha THR) more limited in volume or in their ability to deliver good bass response or both?

I have heard people talk about amps with a tight, focused bottom end vs others that are more flubby (I think that's the term I heard). What contributes to this? It doesn't sound appealing. Does anyone like a flubby bottom or is that just the mark of a lower quality, prersumably less expensive, speaker?

Sorry to go on. I guess if I were going to distill this down to a couple of key questions, they would be, (A) what are the sonic characteristics of different amps that are reflected in something other than frequency characteristics (i.e., something that can't be compensated for by adjusting tone knobs and EQ settings), and (B) which of these other things are modelling amps able (or not able) to model?