The Apple A4 chipset was introduced to the world in April 2010 with the original iPad, and it soon manifested itself in the Apple iPhone 4 as well. At that point in time, this was the fastest processor for smartphones that was available, and it was capable of producing high quality graphics with impressive clocking speeds. Dual-core processors soon started hitting the market though, and the A4 chipset has become a chipset of the past. Apple's new A5 chipset has now been released with the iPad 2, and its dual-core sibling will soon be seen on the Apple iPhone 5 as well.
The Snapdragon chipset is manufactured by Qualcomm, and this is an entire family of chipsets that are used in smartphones, tablets and other devices as well. Both the A4 and the Snapdragon are what are known as SoC, or System on Chips, since they contain processors and graphical processing units as well. This is why they are referred to as chipsets.
