This article is from the Fractal FAQ, by Ermel Stepp firstname.lastname@example.org with numerous contributions by others.
The Mandelbrot set iterates z^2+c with z starting at 0 and varying c.
The Julia set iterates z^2+c for fixed c and varying starting z values. That
is, the Mandelbrot set is in parameter space (c-plane) while the Julia set is
in dynamical or variable space (z-plane).