The "split system" has the air handler (which is the fan with the cooling / heating coil and usually some resistance heat) installed inside and the compressor unit outside. These are connected by copper refrigerant lines. A "package" unit on the other hand has all these parts in one outdoor unit that hooks to ductwork that runs through the outside wall.
if your home has central A/C, you have a split system. you have one part inside and one part outside. they are only connected by refrigerent pipes and wiring. the condensor (radiator) and compressor are outside, and the evaporator (cooler) is inside, usually mounted to the furnace.
a package sytem is used in large stores and factories. the entire unit is outdoors (usually on the roof) and the air ducts pass through to the walls or roof of the building to connect to the equiptment. window A/C units are also a type of package system.
another type of system is called the "mini-split" this is like a split system, but it is of smaller capacity (usually about 2 times as powerful as a window unit) it is split into out door and indoor units. the indoor part does not have any ducting. it simply mounts on the wall. the most common use of a mini-split is when adding A/C to an old building. they are very popular in Japan. they are much quieter than window units and look a lot better too.