Swing Haircut
A: All of the research I've done online suggests that the "swing haircut" refers to a classic wedge, which offers a significant amount of movement in the hair.
If the cut you are referring to is something different, I need to have more information on the cut before I can make any additional suggestions or evaluation. The problem with trying to work from simple "haircut names" is that often these are regional or even more localized terms for a particular style. For example, the basic long-layered haircut is also called a "shag haircut" or a "rocker haircut".
The term by which it is identified depends largely on the area in which you live, or even the salon you go to. It's always advisable to use as much specific information as you have to describe a haircut when talking to a stylist. Communication always generates the best results.
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See also:
How to cut a swing haircut
How to cut a wedge
How to cut hair
Names for hairstyles