The drawing on the left (a) is voltage mode output, the one on the right (b) is current mode output.
The drawings are of 'basic' circuits of course.

The
voltage amp (a) puts out an
output voltage (Uo) that is
proportional to the
input voltage (Ui) by keeping the differential voltage (Ud) the same.
The
current sourceamp provides a
current Io that is
proportional to the
input voltage (Ui) by keeping the differential voltage (Ud) the same Uo = Io x R.
The voltage across the load (the output voltage of the amp - Ud) is now determined by the impedance of that load.
Of course within the limits of the power supply voltage + sensing resistor R's voltage drop.
In the voltage output mode the output voltage is compared with the input (via voltage divider to set the gain).
The current source in the circuit above cannot be used for headphones with a common return wire as they would short the sensing Left and Right channel's sensing resistors thereby f-ing up channel separation.
Theoretically a
current source has an
infinite output Voltage and
infinite output resistance.
Theoretically a
voltage source has an
infinite output current output and
0 Ohm output resistance.
In practice both circuits are of course limited by the power supply or circuit.
Below is the more practical solution when a common ground is needed (single ended headphone)
It is highly likely the HPA-01 is based on this type of circuit.

The output
current (voltage across R1) is now 'compared' to the
input voltage (U R1 = the difference between - and + input + gain of A2 circuit).
The
output voltage will thus
vary depending on the
load impedance and the
driver voltage will therefore be determined by it's
impedance.