differential measurement
Most basic measurements are ground-referenced: you measure the voltage of a point relative to the circuit's ground, with one probe on the node and the implicit other end at 0 V. Differential measurement is when you need the voltage between two points where neither one is ground. Think of it as measuring the height difference between two hills rather than the height of each above sea level. Plenty of important voltages live this way — across a small current-sense resistor sitting up at the supply rail, across a winding, or between the two outputs of a bridge.
Why not just clip the usual probes across the two points? Because a standard oscilloscope is not floating — its ground clip is bonded through the power cord to mains earth. Clip that ground lead onto a node that is not at your circuit's ground and you connect that node straight to earth, which usually means a short circuit, a bang, and damaged parts. The single-channel trick of touching the ground clip wherever you like simply does not work safely on a scope. The right answers are: take two ground-referenced readings and subtract them (use two scope channels in A minus B math), or use a true differential probe — an amplifier that measures the difference between its two tips while keeping both safely isolated from earth.
Why it matters: high-side current sensing, half-bridge switching nodes, and bridge sensors are everywhere in power and motor circuits, and they demand differential technique. The quality measure here is common-mode rejection: how well the method ignores the large voltage common to both points and reports only the small difference. An instrumentation amplifier is the on-board version of the same idea. Two honest cautions: the A-minus-B subtraction loses accuracy when a tiny difference rides on a huge common voltage (small differences between big numbers), and floating a scope by defeating its earth ground to fake a differential measurement is dangerous and must never be done — use a proper differential probe instead.
You want the voltage across a 0.1 ohm sense resistor that sits at the top of a 24 V rail. Both ends of the resistor are near 24 V, but the difference is only tens of millivolts. Clipping a normal scope ground to either end would short 24 V to earth. Instead you use a differential probe, which reads only the small drop while ignoring the 24 V both ends share.
The difference between two live points — done with two channels or a differential probe, never by floating the scope.
Never disconnect a scope's earth ground to make it float for a differential measurement — it puts the whole chassis at the probed voltage and is a genuine shock and fire hazard. Use a proper differential probe or the A-minus-B method instead.