Well based on my knowledge, there is quite a lot of mutations of GCC now, and more are probably out there but have very ambiguous names. "Fancy" in that picture appears to be some FORM of yellowsided ...but it does not look like a true yellowsided that I have seen. With that said, it may be something to do with generations and generations of yellow-sided, or perhaps mixed with other colour mutations. For example, camelot macaws despite having a typical characteristic, vary in a high degree of colour as they are suppose to be mostly yellow from the head to most of the wing, some camelots have green or even red/orange heads. But that picture, I personally do not know, Sorry
I know there are turquoise green cheeks, turquoise yellow sided, yellow sided, pineapple, cinnamon, red factored yellowsided, red factored pineapple, pastel green cheeks, diluted green cheeks etc.
This website:
http://www.feathert.com/newconurecolors.html gives some pictures and explanations regarding colour mutations and how genes will interact to produce GCCs that will show phenotypic or carry genotoypic variations.
The second picture below the "fancy" greencheek appears to be the standard Greencheek. I have a split - split for blue/turquoise GCC that's almost 7 years old and her colours are just slightly different than the standard greencheek, so at the end of the day, expect a multitude of mutations and variety from the GCC specie.
Hoped that helped!
Cheers!