Curling Wand

Conair CD117 curling iron
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.
The term curling iron was likely devised to indicate it's similarity to and ease of use equal to that of a household iron. It takes the mystery out of the concept of using heat styling to curl the hair.
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.
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?