The
only alteration was giving names to the nets, so you can see where the output voltage has to be measured. Nothing more.
out_P and out_N are symbolic names for the nets, so you can easily identify the nets instead of having to look for cryptic net names like n002. You access them in LTSpice by the little symbol with the "A" right next to the GND symbol in the menu bar. A window will pop up, enter a name and attach the symbol to a net.
Not another way, the only correct way. Since GND is connected to the input voltage, any voltage on the secondary side (after the rectifier) referring to GND will see the input voltage's sine as part of the waveform.
By moving GND to the secondary you changed teh reference point for voltage measurements.
As an aside
: Voltage measurements are
always between two points (potentials), never on a single point. You can easily test this by touching one pole of a battery with your tongue: nothing happens. Touch both poles and you will will feel the tickling from the voltage (aka potential difference) between the two poles (Note if you really try this, don't use more than a 1.5V battery!)
We (and LTSPice too) most of the time simplify matters by designating one potential as reference, calling it 0V or GND or similar and form there on reference any voltage measurement to this reference potential. Therefore the "measurement" V(n002) is really V(n002,GND). This is how in my "modified" circuit I measured the output voltage aas the difference between the potentials on out_P and out_N as V(out_P,out_N).
See item 2 in post #49.