Don't know if it helps but:
My 2008 10 FP was a Law Enforcement model with an internal mag.
My 2010 10 FCP-K was a Law Enforcement model with a detachable mag (the C designator) and a muzzle brake (the K designator).
I always assumed that the P designator stood for Police.
The F designator was used on a wide variety of model 10 and Model 110s at the time so I don't know what it might have designated.