OR: is the rating for the entire receptacle or each outlet individually?
A common 15A receptacle has two outlets. If such a receptacle is attached to a 20A circuit, an 8A draw from each outlet will not trip the breaker.
Should such a draw cause the receptacle to fail? Or is the rating for each outlet contained in the receptacle?
No.
For a receptacle to be rated for 15A, it must be able to handle 15A at either outlet. For example. If you plug one item that draws 15A into a receptacle, the receptacle must be able to handle that current.
Receptacles are actually designed to handle 150% over their rated current (or something like that, I'd have to find the specification to be sure). A 15A receptacle should be able to handle 22.5A, so your breaker should trip before the receptacle fails.
Consider this image...
Assuming the tab between the hot terminals is removed, and the red and black wires are each connected to separate 15A breakers. This is a valid configuration, and would allow 15A to be drawn at each outlet.
However, It's usually not a good idea to tempt fate, or stress test electrical components. So in theory, it will not fail. In practice, it should not fail.
It is very common to use a 15A outlet on a 12g 20A circuit. You can go down in rating but you cannot go up. A 15A outlet on a 12g 20A circuit is ok, but a 20A outlet on a 14g 15A circuit is bad. This is to protect the wires in the wall, you want the outlet or breaker to fail before the wire does.
