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

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?


Doesn't actually exist
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.