With the LEDs, the converter is running in a discontinuous mode. There are 3 phases of the operation.
1) When the voltage across the inductor is positive and steady, the current in the inductor is increasing
2) When the voltage across the inductor is negative and steady, the current in the inductor reduces, eventually getting to nothing.
3) The oscillation is when the switches and diodes are not conducting, and there is some oscillation from the inductance and the stray capacitance in the circuit.
Without the LEDs, the converter is running in continuous mode. There are 2 phases of operation.
1) When the voltage across the inductor is positive and steady, the current in the inductor is increasing
2) When the voltage across the inductor is negative and steady, the current in the inductor reduces but does not get to zero.