What is meant by 8-bit resolution on the AD8802's PWM input?
I am using two chips with two different PWM resolutions. The AP8802  (needs 8bit) ...


As per your comment below, this is stated on page 11, paragraph 2:


  A Pulse Width Modulated (PWM) signal with a max resolution of 8-bit, can be applied to the CTRL pin to change the output current to a value
  above or below the nominal average value set by resistor RSET. 




The datasheet is very short on details of the inner workings other than Figure 1. Normally the PWM input would be passed through to the power output stage but the highlighted block suggests an internal low-pass filter (the line through the high and medium waves signifying that they are removed). The control input also has to cope with PWM and regular dimming so there's probably some funky stuff going on inside - but it could be as simple as an R-C filter to average the PWM input into an analog voltage.

The best suggestion I have to offer is that the subsequent block has an 8-bit A/D converter and that there are only 256 discrete output levels available.

For your application you don't have to worry about this. Your 12-bit PWM will be filtered and read by the AP8802 ADC and converted to an 8-bit value internally, effectively losing some of the resolution of the external controller.