First is the standard "drawn" sink. Drawn stainless is a sheet of metal that is placed in a large press(usually 35plus Tons) and then stretched to make the bowl. The "drawing" of the steel comes when the steel is pulled into the sink bowl to help form. The gauge or thickness of the material used is gauged before the bowl is drawn. Thus an 18 Gauge sink is 18 Gauge (or 1.2mm) before the drawing process. The following from Elkay is a great example of drawn stainless steel:
The second type of stainless steel is a Fabricated Sink. This is manufactured by taking a sheet of stainless steel and folding it up with a break press(like a card board box). This produces a straight dimensional sink; commonly used in commercial kitchens or upper end kitchens adapting the commercial look. Here is an example of Blanco stainless steel:
So what are the pros and cons of each type? First the drawn sink is typically less expensive, more readily available and is as reliable as the fabricated sink. The benefit of the fabricated sink is straighter deeper bows and generally heavier in gauge(thickness). The down side of the fabricated sinks is when they are a straight 90 degree corner can be hard to clean. Some manufacturers offer radius corners that give the straight dimensional look with a easy to clean corner. Here is an example of an Oliveri: