The lithosphere is the crust + the rigid upper mantle, while the asthenosphere is deeper and relatively fluid. The asthenosphere is believed to move in convection currents pushing the lithosphere plates.
Similarities:
Both are within 200km depth from the earth's surface.
Both allow Earthquake P-waves to pass through them.
Both are constituted of relatively low density material, mostly silicate (SiO2) rock (Rich in Fe, Mg).
Both are of relatively low temperature compared the the rest of the earth.
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