> How is it you get a fairly wide frequency range from nothing but 12" speakers?
A twelve is naturally flat up to about 800Hz. Above that point, total power output falls, but directivity rises. With light stiff paper, it is not hard to get sorta-flat on-axis to past 3KHz, often strong lumps out to the 5KHz-6KHz range.
The response of a Twelver above ~1.2KHz is real ratty. At first, coverage reduces from 180 deg to 60 deg and getting narrower: not hitting the side of the audience. For hi-fi, it does not "fill the room", a necessity in small-room work. Somewhere around here resonances in the paper cause dips and peaks. At a little higher, an ideal cone's pattern would break-up and throw multiple beams. A real cone, or two of them, will throw a different comb-filter to every place in the room. Comb filters are very audible when swept, but not very harmful when static (when the listener sits still). Everybody gets a slightly different version of the 1.2KHz-5KHz range, but they all get enough to enjoy the music.
Off-axis (anywhere in a room except on-axis), a closed-box Twelve would sound tubby: flat and omni to ~800Hz, then beamy and falling 6dB/oct. However the open-back cabinet has significant bi-di directivity, so it is weak off-axis through the bass-800Hz range. The directivity is fairly uniform from bass to above 2KHz.
The tone stack in a gitar amp allows boosting >2KHz which gives approximate correction for the falling power response and also room effects.
The Fender Twin cabinet is not quite big enough to baffle an 80Hz wave, even counting floor-reflection. 80Hz is down, but speaker resonance is around 80Hz and under-damped which causes a rise.
The net result is that a Fender Twin can be remarkably flat in power output from the lowest gitar note up through low harmonics of the highest note you can fret. The last octave of harmonics is bright on-axis and dull off-axis. Throughout the whole range, directivity gives 6dB-10dB more "throw" than an onmi speaker would.
Amps smaller than a Fender Twin have to compromise. A one-Ten open-back box will not have the balls of a Twin, but if you work with a bass player it may not matter one bit. A open-back Ten will throw your screaming solos just fine. Even smaller, you need to go closed-box to have a pretense of handling the lowest gitar note, so you lose "throw" and get a different balance between on- and off-axis response.
> What is the difference between a guitar amp and a keyboard amp?
Usually the keyboard amp is closed-back, omni in bass, has some throw around 800Hz, then adds a mid-tweet to splatter 2KHz over most of the room, beaming at 8KHz. Straight-up EQ is nominally flat, not treble-shelf boost like a gitar amp. Directivity is lower, frequency response is a little wider: a big KB amp will go 60hz or 50Hz, and the tweet past 8KHz so you can do the space-effects that synths do, without sounding like you phoned it in. I'd be real wary of any "keyboard amp" that didn't have a tweeter, unless you want your synth to sound like a Fender.
Oh, yeah: some guitarists use phatt distortion, most synth just clips.
> satisfactory for both theremin and analog synth
Theremin has special problems due to pure tone, total portamento, and 80 years of tradition. Of course Theremin is so unusual that nobody is going to complain that your sound isn't right. I'm not even sure what to suggest; I expect you will learn that for yourself.
