No, the height of the wedge - which refers to the heel - can vary.
For a shoe to be categorised as a wedge shoe, it needs to have a
wedge heel which is prominent and obviously higher than that of
a traditional shoe. As the picture below shoes, wedge shoes do not
feature any space under the arch of the foot; the sole is basically
flat, but tapers upwards at an angle.
The wedge shoe is mostly seen as a ladies shoe. The minimum heel
height of a wedge shoe is around about two inches; the maximum heel
height is around about six inches. The upper of a wedge shoe - the
material above the sole - varies, and adheres to no specific design;
the only part of a wedge shoe which remains standard, is the design
of the heel, although the angle and height can vary.