Does CFCE count as it's own method.
It's a method for the last layer, why not? It would be absolutely ridicules to call it CFOP because here's the thing, CFOP isn't a word, it's an acronym. If we're going to call CFCE CFOP why not call CFPO or CFEC CFOP? It just doesn't make sense to not allow it its own name.
or is it just a variation of CFOP, like FreeFOP?
I don't understand why you would think this here. Is it a variation of CFOP? Sure, just as much as it's a variation of CFEC and CF1. If you consider a variation of CFOP because CFOP is more popular then there is still a problem with that. CFCE was being used before CFOP meaning that CFOP was probably once considered a variation of CFCE. This is the kind of thing that doesn't change over timer. I'm not saying that CFOP is a variation of CFCE because they solve the last layer in different ways. They are really just LL variations, not of each other. ZBLL, CE, EC, OP, PO, ZZLL, AZBLL, 1LLL, these are all just variations of the last layer.
Now what really (and I mean really) upsets me about his post is that you call FreeFOP a variation of CFOP. I would like to request why you said something so untrue. Are you misinformed? Did you not think it through? Did you create some kind of rationalization for this? FreeFOP involves solving the F2L in whatever order is most efficient. This can involve a Roux block followed by the last three cross edges giving an xxcross. It can involve Cross followed by F2L, it can involve a pseudo style solving. This is all FreeFOP. We get separate methods like CFOP or Petrus when we stop doing it freestyle and instead solving the first two layers in a set way every solve. For FreeFOP you might solve cross followed by F2L, say, 50% of the time but when you do that every single solve it's no longer really FreeFOP because you are not doing it freestyle. So we assign names to subset of FreeFOP. Ultimately every LL method is a subset of a greater method which I like to call FreeFALL (which stands for Freestyle F2L All of Last Layer) where you solve F2L freestyle and do 1LLL. Now, 1LLL is a lot of algorithms. Only one person knows it in its entirety. Because of this we break it into two look or influence the last layer to give us a reduction of cases (this is most often done in the form of ZBLL)
So no, FreeFOP is not a variation of CFOP. CFOP is a subset of FreeFOP which is a subset of FreeFALL which is a subset of F3L (literally just optimal solution).