Just to clear things out. if I understand it correctly, "differential" probes means that they are truly floating, and that they share nothing in common with the other pair, or with the ground or with anything else on your bench.
no, they must share a "common voltage", physically or mathematically and hence "differential voltage" between them will be defined . that will determine the state of the common mode and differential voltage limit of the diff probe. if the common mode voltage rating is exceeded? the probe input fet or bjt will be screwed. if two points have very different common modes (or gnd references, ie as you have put it, "truly floating"), they will manifest in differential voltages, and if that is exceeded? the probe is screwed. even if you try to probe 2 different grounds, for eg earth's ground and mars' ground, the probe will be screwed, because the difference is way off the chart. so technically for differential probing, no 2 points are truly floated, they must be brought to one common term, usually the probe's ground, resistively or capacitively coupled to the inputs.
Which means you can pretty much plug them anywhere without shorting anything out. Is that correct?
correct, albeit the 2 signals are brought common to the probe's gnd, nonetheless at some safe impedance/coupling level, safe if the common mode and differential votage specs are not violated.