Curling Wand
Q: What is the difference between a curling iron and a curling wand?
A: Nothing. The terms curling iron and curling wand indicate the same tool type. The different terms are likely born of a desire to give a specific impression.
Curling Wand was probably a marketing idea designed to invoke some image of hair magic meant to encourage people to buy a particular brand of tool.
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See also:
Heat styling basics
How to style hair with a curling iron
A what's what guide to curling irons
What do I need to look for when buying a curling iron?