Does using 220V-110V transformer matter?
RE: why output of transformer is different ?

The difference is caused by non-ideality of transformers. Most noticable non-ideality is the leakage inductance. For switching load with some cable or filter capacitance like thryristor commutated load, there can be unpredictable runaway mode with circuit resonating at high frequencies.

Another non-idealities of tranformer is non-linearity, caused by saturation, which can clip the original sinusoidal waveform coming from source, asymmetric rectifier, which can magnetize core and saturate it even worse, simple raw peak rush currents, which can overload transformer.

Or for very simple case, it can be manufactures disclaimer to save user from misuse of little 90VA "autotransformer" when they plug 1000W hair dryier and cause all kinds of trouble.

What is the device in question ? Looks like it is something special