When you think of the 2 types of clipping in distortion or overdrive pedals there's two pedals that come to mind. The Ibanez Tube Screamer uses symmetrical clipping and the Boss SD-1 uses asymmetrical amp like clipping.
Symmetrical clipping is considered to have more of a vintage bluesy like tone and asymmetrical has more of a modern tone per say. Here's how it works? The signal from your guitar is an AC voltage made up of positive and negative voltages.
Symmetric clipping clips off the same amount from the positive and negative side of the signal. Asymmetric clipping clips off more of one side of the signal than the other.
It's said that this type of clipping has a more tube-like sound than symmetric clipping. The Tubescreamer and SD-1 have very similar circuits but they clipping stages are different! So you can make a SD-1 into a Tube Screamer or vice versa!