There are 3 yellow face mutations: Type 1, type 2 & golden face. The type 1 is a pale yellow, the golden face is very bright yellow & the type 2 is in between. The best way to identify the different types is by the way the yellow spreads into the body colour. The 3 mutations are unrelated to each other and they are all dominant.
There is quite a bit of disagreement about how yellow face mutations should be described but this makes no difference when working out their inheritance. Some people are adamant that the way they describe them is right but nothing has been properly proven
Like any other dominant mutation more than one type of yellow face can appear on the same bird but you probably wouldn't be able to tell visually if a bird had 2 mutations
the inheritance mostly works like a dominant gene, so understanding what causes yf is not necessary to work out the breeding results luckily... as nev said there is some disagreement.
the only difference from a normal dominant-recessive inheritance pattern i can i think of is with yf1 where a df yf1 has a white face like a non-yf1. the other two act just like you would expect a dominant gene to.
i think there are two theories as to what a yf actually is. some think it is a mutation of the blue gene so that it does not completely lose the yellow. if this is true then a green bird cannot be yellow face, but it can be green/yf blue.
others think it is a completely separate gene that causes the yellow to appear on the blue. in this case any bird, including greens, can be yf but obviously it is not visible on a green...
these differences do make a bit of difference to inheritance but not enough to really confuse things.