The lithosphere is the very top layer of the Earth's crust, while the asthenosphere is the semi-fluid layer just beneath it. The asthenosphere is found between 50 to a few hundred miles below the lithosphere.
The lithosphere is separated into the continental or oceanic crusts and the uppermost layer of the mantle. The crust and the upper mantle are separated by what is called the Mohorovicic discontinuity.
Scientists believe that the oceanic crust is between 31 and 87 miles thick, while the continental crust is between 25 and 174 miles thick. They determine this by noting the depths at which olivine, a silicate mineral, starts to become viscous.
The state of the rocky material in the asthenosphere is similar. Though it is still solid, it is able to flow due to great heat and pressure. Because of this, blocks of the rigid lithosphere "float" on top of the asthenosphere.
Moreover, the oceanic crust is much younger than the continental crust and is made largely of basaltic rock. The continental crust is older and has a greater variety of rock types. This is because the continental crust is less dense than the oceanic crust and the rocks don't sink and rise within the Earth as readily.