What is the difference between these two burden resistor configuration
&quot;the ADC ALWAYS takes differential measurement&quot; that's not true, it's valid only for differential type ADC.
Every signal has to have a reference voltage, usually the GND. Left wiring type should be used where possible (differential ADC), and the right wiring, when you have a single ended ADC, probably you need also to buffer and bias the signal in case the signal comes from current transformer.