What is the difference between Precipitable Water (PW or PWAT) and Quantitive Precipitation Forecast (QPF) in terms of computer weather model data?
Precipitable water is the total amount of moisture throughout the air (the total in the entire tropospheric air "column"; most moisture is found in the lowest few km, due to decreases in temperature and density and where humidity sources being at the ground).  

Whereas QPF is the amount of precipitation that has fallen or is predicted to fall in a certain period of time (often 6 or 24 hours).

Generally more moisture (higher PWATs) do indicate the potential for more precipitation.  But you could definitely have a large PWAT and get no rain/snow/etc to fall from the sky.

I believe the greatest PWAT values are typically found in the warm saturated columns near tropical cyclones (hurricanes/typhoons).  From experience, in the US South, PWATs near/above 2 inches are generally considered quite large in the summer, and tend to indicate a greater chance of rain from air mass/sea breeze/frontal storms.

Whereas hourly rainfall rates can often be nearer 3-5 inches per hour, and locations can report over 20 inches of rain in a day [rainfall records].