This is my impression:
Pinging = sound from resonance that occurs in a switch's
Ringing = sound from resonance that occurs in keyboard plate, PCB and/or perhaps even the case.
... and I think that it can sometimes be very difficult to hear if the sound is ringing or pinging.
I think that it could even be both.
On one keyboard, the ping of a switch could cause ring in the plate, while on another keyboard, a switch that does not ping could cause resonance in the plate, and on a third keyboard a switch could ping but do not normally cause ringing.
Apparently, one switch could cause ringing while another does not. Switches could also ping and ring differently, depending on how you type.
Buckling spring keyboards ping clearly, but they don't ring.
Most of my boards with PCB-mounted Cherry MX blacks ping.. or ring (I don't know which!) when I type normally. Another board with plate-mounted Cherry MX blacks rings/pings loudly, while yet another does not. My Cherry MX Blue, Brown and Clear boards are very silent.