The difference is...

A while ago I posted on wedges and then wore a pair of espadrilles and had to post about the difference... So the difference is this :

Wedges
Describes the type of heel on a shoe - it is a chunky fill under the arch of a shoe forming a heel with "support".  I love these lace up ankle boots in wedge form to lift your spirits this winter!

Image from here.

Espadrilles
Shoe made of some hemp, rope or cord. It is heeled with a moderate platform. Espadrilles generally tie around your ankle with straps or ribbons. These are so beautiful... Well Louis knows best!

Image from here.