What is the difference between Principal Component Factor (PCF), Factor Analysis (FA) and Principal Component Analysis (PCA)?

#1
I understand PCA and FA are both data reduction methods with different assumptions, But when you're extracting the factors using FA, in STATA, you have more than 3 options (FA, PCF, ipf and ML). My concern is on FA, PCF and PCA? how do I differentiate the three?
and can one use both FA and PCF to extract the factors from the same dataset?
 

spunky

Doesn't actually exist
#2
Can you point on where in the STATA documentation they describe these models?

I recognize a few but (with the exception of PCA) those acronyms are meaningless to anyone who doesn't use STATA. We need to know how STATA defines the models to tell the difference.