Differential voltage measurement with Arduino UNO EDITED:
I bought a very sensitive (and expensive) pressure sensor which requires differential analog measurement. I am an amateur hobbyst and a total beginner in Arduino so I would like to ask some advice on how to connect the device so nothing would be damaged.

In the figure below is the scheme which I've got form the manufacturer along with schematic on how I am going to connect that:


the wire colours are as in the provided device,
the symbols are as they were attached to the wires,
the resistor was provided and connected by the manufacturer.


As far as I understood the sensor manual I should connect the device to analog pins as in the schematic below, and read the A0 and A1 and subtract the signal values. Is that fine? Should I connect the wire going to A1 to Arduino GND as well?



Or should I connect the GND instead of A0 line in the image below?


EDIT: Original connection scheme from the DS and link to the CL1A sensor www and  link to the sensor datasheet (only in Polish)
Yeah, possibly I misunderstood something.
You do not need to do any kind of differential measurement here. The
Arduino analog input measures voltages relative to ground. Then, as long
as the Arduino and the power supply share a common ground, you should be
fine.

On the other hand, you may need a voltage divider. I have seen a few
sensors interfaced the same way (GND, +24V and signal), which output a
voltage between 0 and +10&nbsp;V. That could fry the Arduin, and maybe
also the sensor. Check the datasheet to see the maximum voltage the
sensor can output, and use a voltage divider to get that safely into the
0 –&nbsp;+5&nbsp;V range.