The confusion here is that PSRR (Power Supply Rejection Ratio) is a general term which in practice is actually used to refer to multiple things. In general it is a ratio comparing a change in a parameter against a change in the supply's DC voltage level.
For example, PSRR in an ADC is often used to refer to the ratio of the Gain Error to Change in DC Voltage of the Supply.
Some of this comes from confusing the acronym PSRR, which can be used as:
"Power Supply Rejection Ratio" which is, as mentioned above, a ratio between a measured parameter and a change in the supply's DC voltage.
"Power Supply Ripple Rejection" which is the term which is, in general, the ratio of AC voltage on the supply to AC voltage on the input or output. But, this can also be a ratio of an input to an output in the case of something like an Linear Regulator.
Lets look at an example: http://focus.ti.com/lit/ds/symlink/opa121.pdf
Here you'll see in the table on page 2 a value listed under the "Offset Voltage" section as "Supply Rejection".
This is a "Power Supply Rejection Ratio" comparing changes in the supply's DC level to shifts in the output's offset voltage.
On page 3 a value listed under the "Input Offset Voltage" section as "Supply Rejection".
This is a "Power Supply Rejection Ratio" comparing changes in the supply level to shifts in the input offset voltage.
Looking at charts on page 4, we see a graph of "Power Supply Rejection vs Frequency".
This is a "Power Supply Ripple Rejection" measurement of AC ripple rejection which is the ratio of Supply Ripple to Input Ripple.
This last one may be a bit confusing as for an op-amp the "Power Supply Ripple Rejection" is often specified as a ratio of the supply ripple to the input ripple. This will generally be the case for devices with feedback or in the case of an op-amp, are generally used with feedback.
For devices without feedback, class D audio amplifiers for instance, "Power Supply Ripple Rejection" is usually just a ratio of the supply ripple to the output ripple and "Power Supply Rejection Ratio" is a measurement of the impact on the supply DC level to the output offset voltage.
In summary there isn't really a hard and fast definition for 'PSRR' and often other terms are used such as 'Supply Rejection', 'Ripple Rejection', 'Power Supply Rejection', etc. The important thing is that they are always measurements describing the effect of the power supply on the circuit in question. To figure out what the measurement really means you have to consider the context of the measurement as well as the mode of operation of the device.
EDIT: Here are some examples of different uses by manufacturer:
National Semiconductor: Uses the terms "Power Supply Rejection Ratio" for AC and "DC Power Supply Rejection Ratio" for DC.
Maxim: Uses "Power Supply Rejection Ratio" for DC and "Ripple Rejection" for AC
TI: Uses "Power Supply Ripple Rejection (PSRR)" LDOs and Various forms of "Supply Rejection" for Op-amps (see data sheet above).
Analog Devices: Uses "Power Supply Rejection Ratio" defines it as relating to either the input or output, and even argues that the term PSRR shouldn't be used if its expressed in dB but rather PSR (Power Supply Rejection) should.
There are many more examples but I'll leave it at that.
So again, there really is no standardized definition here, its all up to context.