What is the difference between magnetic stripping and magnetic field reversal?

Magnetic stripes are evidence of the magnetic field reversal. It's sort of like saying that bear tracks in the snow are evidence that a bear walked by.
Magnetic stripes on the seafloor are formed when new ocean crust is formed. As the magma erupts from the mid-ocean ridges and cools to form rock any minerals containing iron will be oriented in the direction of the magnetic field. When the Earth's magnetic field reverses (every million years or so) the new rock that gets formed will have its magnetic minerals oriented in the opposite direction. This results in a series of magnetic stripes in the rock on the seafloor. (Think of it kind of like a bar code.)
Because new ocean floor is being formed on both sides of mid-ocean ridges and spreading away from the ridges as even newer seafloor is formed, there are symmetric stripes on each side of the ridge. This led to some of the early evidence of tectonic plate motion.