You're right as to what AVR stands for. I think the best way to think about is that the AVR is an active electronic system, where the capacitor is more of a passive, reactive method.Now then, I thought AVR simply stood for Automatic Voltage Regulator. Why the capacitor type might be considered as non-automatic, I’m not sure. Need an explanation please, as I always think automatic control is simply the opposite/alternative to manual control.
A decent AVR maintains the voltage not just regardless of the load applied (within the capabilities of the machine), but also over quite a wide speed/frequency variation, where the capacitor alternators voltage output rises with more speed, and drops with a falling frequency. Also the capacitor machines can gain volts as a small load is applied, where an AVR set shouldn't vary.
(There's a 3rd type - a transformer winding voltage control that's rarely seen now. Great fir big motor start and impact loads, but like capacitors, the regulation is rather crude and not tight like a good AVR system).
Often, lots of electrical loads are very tolerant of voltage variation - so you can get away with a lot - but electronics are often the most demanding/particular.