Why does only class C airspace have an "outer area"?
The Class C outer area is the airspace surrounding Class C airspace out to 20nm, and from the lower limit of radar coverage to the top of the controller's airspace.  The outer area is not charted, although you can see in the white boxes (in the chart below) adjacent to Class C airports that you can initiate communication within 20nm.

ATC offers Class C services (e.g., flight following) on a workload-permitting basis to participating aircraft operating in the outer area, and aircraft in 2-way radio communication will receive IFR/VFR aircraft separation services.
So you can think of Class C airspace as 3 concentric rings: the 20nm outer area, the 10nm shelf area, and the 5nm surface area.
Source AIM 3-2-4