A vortex is a spinning, often turbulent, flow (or any spiral motion) with closed streamlines. The shape of media or mass swirling rapidly around a center forms a vortex. It flows in a circular motion.
Wake is the distrubed airflow downstream from the object. If the vortex trails far enough behind the object, we can have a wake vortex.
This is a good photo of a wake vortex.
And in this photo, note the blue vortex formed along the fuselage strakes. In this scenario they are carefully controlled, to give a substantial low pressure zone along the top of the strake.
http://www.fluidmech.net/gallery/vortex/w_tun.htm
)
