This is probably a dumb question, but in what way do semi acoustics sound fundamentally different to a regular electric guitar when amplified in a large setting - since pickups amplify the signal from the strings and not the actual sound being produced by the hollow body?
The strings don't vibrate all by themselves. They vibrate very differently based on the properties of the guitar they're on. Things like the wood density and geometry affect how the string behaves when it's plucked, so the attack and sustain can vary an awful lot. Different species of woods, and materials used in the hardware, also have different resonant peaks, which mean that they will vibrate with the string's various harmonics and cause emphasis on different frequencies, like there's a tiny little passive equalizer for every component of the guitar.