Hello.. Sorry for the late response, errands today. Well the answer to both questions is a yes and you are correct and they are correct. As far as the mohawk it is determined by the cut yet, however if it was styled differently it could be called something else. That being said however if the sides are shaved and there is a 1-2 area of hair on the top and down the back it is definitely a mohawk. Also if the Occipital ( back) is shaved the combed back version would be considered a Norse, or Viking Cut, and once stood up a 1/2 mohawk.
As to the Pompadour that is a style, as that haircut can be worn in so many ways. Pompadour is height in the style with a back comb and tradionally a "Duck Arse" in tha bacl similar to the tail feather of a duck. Modern styles keep a short side and 6-7 inches on the top that can be "pomped"
In Summary:
Mohawk: Both answers are correct with the Viking Caveat, meaning shaved or short just above the occipital ridge on the back
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Pompadour is a style:
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but KJ you could with actually style your hair into a modern pomp as well