The Signal Recovery Model 5184 is an ultra low noise preamplifier. The product description says
... and incorporates a special pseudodifferential input stage that can be floated to give the ground loop immunity normally associated with true differential inputs but without the associated noise penalty.
The question is
Typically pseudo-differential inputs have an asymmetrical input impedance- much lower for the 'low end' of the input. In this case, it only allows 300mV of common mode voltage. I didn't read the manual fully, but some instruments have 50 ohms relative to ground, which is high enough to prevent serious interference from ground loops.
Of course a fully differential input stage will have a higher noise, the textbook amount is \$\sqrt{2}\$ higher for two inputs subtracted with uncorrelated noise source in each.
This particular instrument has a JFET input with very low white noise (0.8nV/\$\sqrt{\text{Hz}}\$ @ 1KHz), so the ~40% improvement is worthwhile.
Note that they are targeting cryogenics, where the classic Johnson-Nyquist source noise will have much lower power for a given source resistance than at room temperature (noise power spectral density is proportional to the absolute temperature), so you would like to have an amplifier with a low noise temperature and high input impedance. That combination might not make sense at room temperature, at least without a transformer.
Edit: Without getting into the exact topologies of a low noise preamp- the pseudo-differential input low is essentially an internal ground- there is zero noise from it- by definition- because it is the reference point. The high input goes to the JFET gate, and a good JFET contributes noise of < 1nV\$\sqrt{\text{Hz}}\$ above the corner frequency. A differential front end would require two JFETs (such as a differential long-tailed pair) and each would contribute similar amounts of noise, so 1.4 times higher noise. I'm ignoring the exact topology and the necessary feedback path, but it should be obvious that the feedback path can be via a passive low-impedance divider (for example, to the JFET source) and thus will not be a contributor to the noise other than the noise from the resistors (which can be made relatively small- perhaps a few ohms- so its noise contribution is << 1nV\$\sqrt{\text{Hz}}\$. Ground-referencing the signal would take place after amplification, so the noise contribution from that is negligible.
For a possibly more familiar example using op-amps, compare these two:
simulate this circuit – Schematic created using CircuitLab
The input-referred noise of the single-ended gain of 100 amplifier will be approximately 1/sqrt(2) of the noise of the fully differential instrumentation amplifier with the same gain because the \$e_n\$ of the two amplifiers add in quadrature.
