I'd call 5/0 classic blitz.
OTB, I agree. Online, you do not need to reset the pieces you knocked over, nor press the button on the clock. For me, thus, 3 0 online is closer to 5 0 OTB.
Those old BHB clocks would spin on the table in the donut shop when players were under a minute. One guy glued some foam on the bottom of his to prevent this.
I've played it OTB with analogic clocks. Really funny, although I'm really bad at it.