Both blanking and piercing are essentially the same thing: A process whereby a particular shape is punched out of a sheet of metal, just like a cookie cutter and a sheet of dough. The difference is that with blanking the outside part is waste, whereas with piercing the inside part is waste--it's an is-the-glass-half-full-or-half-empty kind of thing.

Blanking is often the first step in turning a raw material into a finished product and is rarely the last, except for simple components like, say, washers. But much of the time the blank will then undergo another process to make it into its final form. An example of this is a metal circle being blanked, and the resultant disc then drawn into a bowl shape, and the bowl then perforated (see explanation below) to make a colander.

Piercing has variations in how it can be applied. For example, to pierce rows of vent holes in a sheet of metal (to make a heater cover, for instance) is referred to as "lancing...."

...while punching a bunch of holes into something, like the Mac Pro casing, is called "perforating."

However, when my ex-girlfriend would punch holes in my arguments for why we shouldn't move in together, I called that "nagging."