It even happens at the cable level. I've had a couple of devices (Galaxy S3, Mophie) that required me to the use the proper higher-quality cable, despite being standard micro USB.

If i recall correctly, that's because the basic signaling for USB charging is resistance based. Too high a resistance on the wire, and it may heat up (even melt the plastic wrapping) if they try to draw more than the default 500mA USB amount.

I believe that higher currents are negotiated with digital signalling. Does that allow for the two ends talk to each other to determine the performance of a cable between them? The Apple lightning cables themselves include a chip.

Anyway, an interesting thing about USB C (and maybe 3.0, too) is that it can also negotiate 12 or 20 volts and even up to 5 amps. For the same wattage, a higher voltage will heat the cable less.

Its a bit of both.

If the data pins are shorted facing the device (so that the device detects its own outgoing signal on the incoming pin) it will consider the port a dumb charger port and attempt to charge from it based on the cable quality.

If there is a proper port response, and the port claim to be a charging port, the device can ask for more than 500mA in increments of 100mA. There will be limitations depending on there being ongoing data traffic or not.

USB 3 cables identify their current capacity through resistive values on the ID pin. Voltage negotiation is also permitted for USB 2 although I doubt it's used much outside of niche products designed to work together.