can speak for waveform in 2nd picture only. perfectly fine for a buck converter that's running under lighter load than it was designed for.
this is called "discontinuous mode", because the inductor is "running out of steam" during the free-wheeling phase, and then resonating with the circuit's stray capacitances.
if fast step response is not an issue in your circuit, you can basically increase the inductance to a value such that the inductor current still hasn't fully vanished at the beginning of the next ON phase. then the inductor current is never going back to zero, and the buck converter will run in "continuous mode". in continuous mode, the voltage in the 2nd picture will change to a clean (if pcb layout is good) square wave.